حلول الأسئلة

السؤال

استعمل معادلة مصفوفية لحل كل نظام إن أمكن فيما يأتي:

الحل

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 2 y minus 4 x equals 3 end cell row blank cell 4 x minus 3 y equals negative 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 4 end cell 2 row 4 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 3 row cell negative 6 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 4 right parenthesis left parenthesis negative 3 right parenthesis minus left parenthesis 4 right parenthesis left parenthesis 2 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell end table end cell blank end table close square brackets equals 1 fourth open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 4 end cell 2 row 4 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 3 row cell negative 6 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 3 over 4 end cell row 3 end table end cell blank end table close square brackets end cell row blank cell x equals 3 over 4 comma y equals 3 end cell end table

شاهد حلول جميع الاسئلة

تدرب وحل المسائل

تدرب وحل المسائل

حدد ما إذا كانت كل من المصفوفتين تمثل نظيراً ضربياً للأخرى فيما يأتي:

9)

K with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 2 row 3 0 end table end cell blank end table close square brackets comma L with _ below equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 0 1 row 2 cell negative 1 end cell end table end cell blank end table close square brackets

K with _ below times L with _ below equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 2 row 3 0 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 0 1 row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 0 plus 4 end cell cell 1 minus 2 end cell row cell 0 plus 0 end cell cell 3 plus 0 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 4 cell negative 1 end cell row 0 3 end table end cell blank end table close square brackets not equal to I with _ below

لا تمثل نظيراً ضربياً.

10)

M with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 2 row 4 5 end table end cell blank end table close square brackets comma N with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 1 row 0 0 end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell M with _ below times N with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 2 row 4 5 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 1 row 0 0 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0 plus 0 end cell cell 0 plus 0 end cell row cell 4 plus 0 end cell cell 4 plus 0 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 0 row 4 4 end table end cell blank end table close square brackets end cell row blank cell N with _ below times M with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 1 row 0 0 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 2 row 4 5 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0 plus 4 end cell cell 2 plus 5 end cell row cell 0 plus 0 end cell cell 0 plus 0 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 4 7 row 0 0 end table end cell blank end table close square brackets end cell end table

لا تمثل نظيراً ضربياً.

11)

R with _ below equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell 1 half end cell cell negative 1 fourth end cell row cell 1 fourth end cell cell negative 1 half end cell end table end cell blank end table close square brackets comma S with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 4 row 4 2 end table end cell blank end table close square brackets

R with _ below times S with _ below equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 half end cell cell negative 1 fourth end cell row cell 1 fourth end cell cell negative 1 half end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 4 row 4 2 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 plus left parenthesis negative 1 right parenthesis end cell cell 2 plus left parenthesis negative 1 half right parenthesis end cell row cell 1 half plus left parenthesis negative 2 right parenthesis end cell cell 1 plus left parenthesis negative 1 right parenthesis end cell end table end cell blank end table close square brackets open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 0 cell 3 over 2 end cell row cell negative 3 over 2 end cell 0 end table end cell blank end table close square brackets not equal to I with _ below

لا تمثل نظيراً ضربياً.

أوجد النظير الضربي لكل مصفوفة فيما يأتي إن وجد:

12)

A with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 0 row 0 2 end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open vertical bar table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 0 row 0 2 end table end cell end table close vertical bar equals 6 minus 0 equals 6 not equal to 0 end cell row blank cell P with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row d cell negative b end cell row cell negative c end cell a end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 3 right parenthesis left parenthesis 2 right parenthesis minus left parenthesis 0 right parenthesis left parenthesis 0 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 0 row 0 3 end table end cell blank end table close square brackets equals 1 over 6 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 0 row 0 3 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 1 third end cell 0 row 0 cell 1 half end cell end table end cell blank end table close square brackets end cell end table

13)

A with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 3 row 3 2 end table end cell blank end table close square brackets

A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis minus left parenthesis 3 right parenthesis left parenthesis 3 right parenthesis end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 2 cell negative 3 end cell row cell negative 3 end cell 2 end table end cell blank end table close square brackets equals fraction numerator 1 over denominator negative 5 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 2 cell negative 3 end cell row cell negative 3 end cell 2 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 2 over 5 end cell cell 3 over 5 end cell row cell 3 over 5 end cell cell negative 2 over 5 end cell end table end cell blank end table close square brackets

14)

A equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row cell negative 6 end cell cell negative 1 end cell end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell A with _ below equals open vertical bar table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row cell negative 6 end cell cell negative 1 end cell end table end cell end table close vertical bar equals negative 1 minus 6 equals negative 7 end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 7 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 1 row 6 1 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 7 end cell cell negative 1 over 7 end cell row cell negative 6 over 7 end cell cell negative 1 over 7 end cell end table end cell blank end table close square brackets end cell end table

15)

open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 5 end cell cell negative 4 end cell row 4 2 end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell A with _ below equals open vertical bar table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 5 end cell cell negative 4 end cell row 4 2 end table end cell end table close vertical bar equals negative 10 plus 16 equals 6 end cell row blank cell A with _ below to the power of negative 1 end exponent equals 1 over 6 open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 2 4 row cell negative 4 end cell cell negative 5 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 2 over 6 end cell cell 4 over 6 end cell row cell fraction numerator negative 4 over denominator 6 end fraction end cell cell fraction numerator negative 5 over denominator 6 end fraction end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 third end cell cell 2 over 3 end cell row cell negative 2 over 3 end cell cell negative 5 over 6 end cell end table end cell blank end table close square brackets end cell end table

16) مشتريات: دفع سعد 225 ريالاً لشراء 5 أقلام حبر جافة و6 أقلام حبر سائلة بينما دفع ماجد 120 ريالاً لشراء 3 أقلام جافة من النوع نفسه و3 أقلام سائلة من النوع نفسه فإذا كان سعر القلم الجاف x وسعر القلم السائل y فاستعمل معادلة مصفوفية لإيجاد سعر القلم الجاف.

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell table attributes columnalign right columnspacing 1em end attributes row cell 5 x plus 6 y equals 250 end cell row cell 3 x plus 3 y equals 120 end cell end table end cell row blank cell vertical line C with _ below vertical line equals open vertical bar table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 6 row 3 3 end table end cell end table close vertical bar equals 15 minus 18 equals negative 3 end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 3 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 6 end cell row cell negative 3 end cell 5 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 2 row 1 cell negative 5 over 3 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 2 row 1 cell negative 5 over 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 6 row 3 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 2 row 1 cell negative 5 over 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 250 row 120 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 5 plus 6 end cell cell negative 6 plus 6 end cell row cell 5 minus 5 end cell cell 6 minus 5 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 250 plus 240 end cell row cell 250 minus 200 end cell end table end cell blank end table close square brackets end cell end table

open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell negative 10 end cell row 50 end table end cell blank end table close square brackets space of 1em x equals negative 10 comma y equals 50

17) سكان: يبين الشكل الآتي نسبة الهجرة السنوية بين إحدى المدن وضواحيها.

نسبة الهجرة

اكتب مصفوفة تبين نسبة المهاجرين والباقين في كل من المدينة والضواحي.

table attributes columnalign right columnspacing 1em end attributes row blank row cell text المدينة end text end cell row cell text الضواحي end text end cell end table open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0.95 end cell cell 0.03 end cell row cell 0.05 end cell cell 0.97 end cell end table end cell blank end table close s

استعمل معادلة مصفوفية لحل كل نظام إن أمكن فيما يأتي:

18)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell negative x plus y equals 4 end cell row blank cell negative x plus y equals negative 4 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign left columnspacing 1em end attributes row cell negative x plus y end cell row cell negative x plus y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 4 row cell negative 4 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 1 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 4 row cell negative 4 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis minus left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets equals 1 over 0 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets end cell end table

ليس لها حل.

19)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell negative x plus y equals 3 end cell row blank cell negative 2 x plus y equals 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative x plus y end cell row cell negative 2 x plus y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 2 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis minus left parenthesis negative 2 right parenthesis left parenthesis 1 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals 1 over 1 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 2 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 3 end cell row 0 end table end cell blank end table close square brackets end cell row blank cell x equals negative 3 end cell row blank cell y equals 0 end cell end table

20)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell x plus y equals 4 end cell row blank cell negative 4 x plus y equals 9 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell x plus y end cell row cell negative 4 x plus y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 4 row 9 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 1 row cell negative 4 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals table attributes columnspacing 1em end attributes row 4 row 9 end table end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis minus left parenthesis negative 4 right parenthesis left parenthesis 1 right parenthesis end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row 4 1 end table end cell blank end table close square brackets equals 1 fifth open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row 4 1 end table end cell blank end table close square brackets end cell row blank cell equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth end cell cell negative 1 fifth end cell row cell 4 over 5 end cell cell 1 fifth end cell end table end cell blank end table close square brackets end cell row blank cell left square bracket open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth end cell cell negative 1 fifth end cell row cell 4 over 5 end cell cell 1 fifth end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 1 row cell negative 4 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth end cell cell negative 1 fifth end cell row cell 4 over 5 end cell cell 1 fifth end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 4 row 9 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth plus 4 over 5 end cell cell 1 fifth minus 1 fifth end cell row cell 4 over 5 minus 4 over 5 end cell cell 4 over 5 plus 1 fifth end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 4 over 5 minus 9 over 5 end cell row cell 16 over 5 plus 9 over 5 end cell end table end cell blank end table close square brackets end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times equals open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 1 end cell row 5 end table end cell blank end table close square brackets end cell row blank cell x equals negative 1 end cell row blank cell y equals 5 end cell end table

21)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 3 x plus y equals 3 end cell row blank cell 5 x plus 3 y equals 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 3 x plus y end cell row cell 5 x plus 3 y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 1 row 5 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator 9 minus 5 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 1 end cell row cell negative 5 end cell 3 end table end cell blank end table close square brackets equals 1 fourth open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 1 end cell row cell negative 5 end cell 3 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 5 over 4 end cell cell 3 over 4 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 5 over 4 end cell cell 3 over 4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 1 row 5 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 5 over 4 end cell cell 3 over 4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell 3 over 4 end cell row cell 3 over 4 end cell end table end cell blank end table close square brackets end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell x equals 3 over 4 end cell row blank cell y equals 3 over 4 end cell end table

22)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell space of 1em table attributes columnspacing 1em end attributes row cell y minus x equals 5 end cell row cell 2 y minus 2 x equals 8 end cell end table end cell row blank cell negative x plus y equals 5 end cell row blank cell negative 2 x plus 2 y equals 8 end cell row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative x plus y end cell row cell negative 2 x plus 2 y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 5 row 8 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 2 end cell 2 end table end cell blank end table close square brackets open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 5 row 8 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 2 plus 2 end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals 1 over 0 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets end cell end table

ليس لها حل.

23)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 4 x plus 2 y equals 6 end cell row blank cell 6 x minus 3 y equals 9 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 4 2 row 6 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 6 row 9 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 12 minus 12 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 6 end cell 4 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 8 end cell cell 1 over 12 end cell row cell 1 fourth end cell cell negative 1 over 6 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 8 end cell cell 1 over 12 end cell row cell 1 fourth end cell cell negative 1 over 6 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 4 2 row 6 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 8 end cell cell 1 over 12 end cell row cell 1 fourth end cell cell negative 1 over 6 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row 6 row 9 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell 3 over 2 end cell row 0 end table end cell blank end table close square brackets space of 1em x equals 3 over 2 comma y equals 0 end cell end table

24)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 1.6 y minus 0.2 x equals 1 end cell row blank cell 0.4 y minus 0.1 x equals 0.5 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 0.2 end cell cell 1.6 end cell row cell negative 0.1 end cell cell 0.4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 1 row cell 0.5 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 0.2 right parenthesis left parenthesis 0.4 right parenthesis minus left parenthesis negative 0.1 right parenthesis left parenthesis 1.6 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0.4 end cell cell negative 1.6 end cell row cell 0.1 end cell cell negative 0.2 end cell end table end cell blank end table close square brackets equals fraction numerator 1 over denominator 0.08 end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0.4 end cell cell negative 1.6 end cell row cell 0.1 end cell cell negative 0.2 end cell end table end cell blank end table close square brackets end cell row blank cell space of 1em open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell fraction numerator 0.4 over denominator 0.08 end fraction end cell cell fraction numerator negative 1.6 over denominator 0.08 end fraction end cell row cell fraction numerator 0.1 over denominator 0.08 end fraction end cell cell fraction numerator negative 0.2 over denominator 0.08 end fraction end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 cell negative 20 end cell row cell 1.25 end cell cell negative 2.5 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 cell negative 20 end cell row cell 1.25 end cell cell negative 2.5 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 0.2 end cell cell 1.6 end cell row cell negative 0.1 end cell cell 0.4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 cell negative 20 end cell row cell 1.25 end cell cell negative 2.5 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 1 row cell 0.5 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 plus 2 end cell cell 8 minus 8 end cell row cell negative 0.25 plus 0.25 end cell cell 2 minus 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 5 minus 10 end cell row cell 1.25 minus 1.25 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 5 end cell row 0 end table end cell blank end table close square brackets end cell end table

25)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell table attributes columnalign right columnspacing 1em end attributes row cell 4 y minus x equals negative 2 end cell row cell 3 y minus x equals 6 end cell end table end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 4 row cell negative 1 end cell 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 2 end cell row 6 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 3 minus left parenthesis negative 4 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 4 row cell negative 1 end cell 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 2 end cell row 6 end table end cell blank end table close square brackets end cell end table

open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell negative 30 end cell row cell negative 8 end cell end table end cell blank end table close square brackets space of 1em x equals negative 30 comma y equals negative 8

26)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 2 y minus 4 x equals 3 end cell row blank cell 4 x minus 3 y equals negative 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 4 end cell 2 row 4 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 3 row cell negative 6 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 4 right parenthesis left parenthesis negative 3 right parenthesis minus left parenthesis 4 right parenthesis left parenthesis 2 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell end table end cell blank end table close square brackets equals 1 fourth open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 4 end cell 2 row 4 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 3 row cell negative 6 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 3 over 4 end cell row 3 end table end cell blank end table close square brackets end cell row blank cell x equals 3 over 4 comma y equals 3 end cell end table

مشاركة الدرس

السؤال

استعمل معادلة مصفوفية لحل كل نظام إن أمكن فيما يأتي:

الحل

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 2 y minus 4 x equals 3 end cell row blank cell 4 x minus 3 y equals negative 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 2 y minus 4 x equals 3 end cell row blank cell 4 x minus 3 y equals negative 6 end cell end table

تدرب وحل المسائل

تدرب وحل المسائل

حدد ما إذا كانت كل من المصفوفتين تمثل نظيراً ضربياً للأخرى فيما يأتي:

9)

K with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 2 row 3 0 end table end cell blank end table close square brackets comma L with _ below equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 0 1 row 2 cell negative 1 end cell end table end cell blank end table close square brackets

K with _ below times L with _ below equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 2 row 3 0 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 0 1 row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 0 plus 4 end cell cell 1 minus 2 end cell row cell 0 plus 0 end cell cell 3 plus 0 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 4 cell negative 1 end cell row 0 3 end table end cell blank end table close square brackets not equal to I with _ below

لا تمثل نظيراً ضربياً.

10)

M with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 2 row 4 5 end table end cell blank end table close square brackets comma N with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 1 row 0 0 end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell M with _ below times N with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 2 row 4 5 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 1 row 0 0 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0 plus 0 end cell cell 0 plus 0 end cell row cell 4 plus 0 end cell cell 4 plus 0 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 0 row 4 4 end table end cell blank end table close square brackets end cell row blank cell N with _ below times M with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 1 row 0 0 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 0 2 row 4 5 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0 plus 4 end cell cell 2 plus 5 end cell row cell 0 plus 0 end cell cell 0 plus 0 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 4 7 row 0 0 end table end cell blank end table close square brackets end cell end table

لا تمثل نظيراً ضربياً.

11)

R with _ below equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell 1 half end cell cell negative 1 fourth end cell row cell 1 fourth end cell cell negative 1 half end cell end table end cell blank end table close square brackets comma S with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 4 row 4 2 end table end cell blank end table close square brackets

R with _ below times S with _ below equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 half end cell cell negative 1 fourth end cell row cell 1 fourth end cell cell negative 1 half end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 4 row 4 2 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 plus left parenthesis negative 1 right parenthesis end cell cell 2 plus left parenthesis negative 1 half right parenthesis end cell row cell 1 half plus left parenthesis negative 2 right parenthesis end cell cell 1 plus left parenthesis negative 1 right parenthesis end cell end table end cell blank end table close square brackets open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 0 cell 3 over 2 end cell row cell negative 3 over 2 end cell 0 end table end cell blank end table close square brackets not equal to I with _ below

لا تمثل نظيراً ضربياً.

أوجد النظير الضربي لكل مصفوفة فيما يأتي إن وجد:

12)

A with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 0 row 0 2 end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open vertical bar table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 0 row 0 2 end table end cell end table close vertical bar equals 6 minus 0 equals 6 not equal to 0 end cell row blank cell P with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row d cell negative b end cell row cell negative c end cell a end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 3 right parenthesis left parenthesis 2 right parenthesis minus left parenthesis 0 right parenthesis left parenthesis 0 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 0 row 0 3 end table end cell blank end table close square brackets equals 1 over 6 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 0 row 0 3 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 1 third end cell 0 row 0 cell 1 half end cell end table end cell blank end table close square brackets end cell end table

13)

A with _ below equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 3 row 3 2 end table end cell blank end table close square brackets

A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis minus left parenthesis 3 right parenthesis left parenthesis 3 right parenthesis end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 2 cell negative 3 end cell row cell negative 3 end cell 2 end table end cell blank end table close square brackets equals fraction numerator 1 over denominator negative 5 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 2 cell negative 3 end cell row cell negative 3 end cell 2 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 2 over 5 end cell cell 3 over 5 end cell row cell 3 over 5 end cell cell negative 2 over 5 end cell end table end cell blank end table close square brackets

14)

A equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row cell negative 6 end cell cell negative 1 end cell end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell A with _ below equals open vertical bar table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row cell negative 6 end cell cell negative 1 end cell end table end cell end table close vertical bar equals negative 1 minus 6 equals negative 7 end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 7 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 1 row 6 1 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 7 end cell cell negative 1 over 7 end cell row cell negative 6 over 7 end cell cell negative 1 over 7 end cell end table end cell blank end table close square brackets end cell end table

15)

open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 5 end cell cell negative 4 end cell row 4 2 end table end cell blank end table close square brackets

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell A with _ below equals open vertical bar table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 5 end cell cell negative 4 end cell row 4 2 end table end cell end table close vertical bar equals negative 10 plus 16 equals 6 end cell row blank cell A with _ below to the power of negative 1 end exponent equals 1 over 6 open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 2 4 row cell negative 4 end cell cell negative 5 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 2 over 6 end cell cell 4 over 6 end cell row cell fraction numerator negative 4 over denominator 6 end fraction end cell cell fraction numerator negative 5 over denominator 6 end fraction end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 third end cell cell 2 over 3 end cell row cell negative 2 over 3 end cell cell negative 5 over 6 end cell end table end cell blank end table close square brackets end cell end table

16) مشتريات: دفع سعد 225 ريالاً لشراء 5 أقلام حبر جافة و6 أقلام حبر سائلة بينما دفع ماجد 120 ريالاً لشراء 3 أقلام جافة من النوع نفسه و3 أقلام سائلة من النوع نفسه فإذا كان سعر القلم الجاف x وسعر القلم السائل y فاستعمل معادلة مصفوفية لإيجاد سعر القلم الجاف.

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell table attributes columnalign right columnspacing 1em end attributes row cell 5 x plus 6 y equals 250 end cell row cell 3 x plus 3 y equals 120 end cell end table end cell row blank cell vertical line C with _ below vertical line equals open vertical bar table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 6 row 3 3 end table end cell end table close vertical bar equals 15 minus 18 equals negative 3 end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 3 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 6 end cell row cell negative 3 end cell 5 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 2 row 1 cell negative 5 over 3 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 2 row 1 cell negative 5 over 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 6 row 3 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 end cell 2 row 1 cell negative 5 over 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 250 row 120 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 5 plus 6 end cell cell negative 6 plus 6 end cell row cell 5 minus 5 end cell cell 6 minus 5 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 250 plus 240 end cell row cell 250 minus 200 end cell end table end cell blank end table close square brackets end cell end table

open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell negative 10 end cell row 50 end table end cell blank end table close square brackets space of 1em x equals negative 10 comma y equals 50

17) سكان: يبين الشكل الآتي نسبة الهجرة السنوية بين إحدى المدن وضواحيها.

نسبة الهجرة

اكتب مصفوفة تبين نسبة المهاجرين والباقين في كل من المدينة والضواحي.

table attributes columnalign right columnspacing 1em end attributes row blank row cell text المدينة end text end cell row cell text الضواحي end text end cell end table open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0.95 end cell cell 0.03 end cell row cell 0.05 end cell cell 0.97 end cell end table end cell blank end table close s

استعمل معادلة مصفوفية لحل كل نظام إن أمكن فيما يأتي:

18)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell negative x plus y equals 4 end cell row blank cell negative x plus y equals negative 4 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign left columnspacing 1em end attributes row cell negative x plus y end cell row cell negative x plus y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 4 row cell negative 4 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 1 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 4 row cell negative 4 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis minus left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets equals 1 over 0 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets end cell end table

ليس لها حل.

19)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell negative x plus y equals 3 end cell row blank cell negative 2 x plus y equals 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative x plus y end cell row cell negative 2 x plus y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 2 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis minus left parenthesis negative 2 right parenthesis left parenthesis 1 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals 1 over 1 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 2 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 3 end cell row 0 end table end cell blank end table close square brackets end cell row blank cell x equals negative 3 end cell row blank cell y equals 0 end cell end table

20)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell x plus y equals 4 end cell row blank cell negative 4 x plus y equals 9 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell x plus y end cell row cell negative 4 x plus y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 4 row 9 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 1 row cell negative 4 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals table attributes columnspacing 1em end attributes row 4 row 9 end table end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis minus left parenthesis negative 4 right parenthesis left parenthesis 1 right parenthesis end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row 4 1 end table end cell blank end table close square brackets equals 1 fifth open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 cell negative 1 end cell row 4 1 end table end cell blank end table close square brackets end cell row blank cell equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth end cell cell negative 1 fifth end cell row cell 4 over 5 end cell cell 1 fifth end cell end table end cell blank end table close square brackets end cell row blank cell left square bracket open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth end cell cell negative 1 fifth end cell row cell 4 over 5 end cell cell 1 fifth end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 1 row cell negative 4 end cell 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth end cell cell negative 1 fifth end cell row cell 4 over 5 end cell cell 1 fifth end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 4 row 9 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 fifth plus 4 over 5 end cell cell 1 fifth minus 1 fifth end cell row cell 4 over 5 minus 4 over 5 end cell cell 4 over 5 plus 1 fifth end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 4 over 5 minus 9 over 5 end cell row cell 16 over 5 plus 9 over 5 end cell end table end cell blank end table close square brackets end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times equals open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 1 end cell row 5 end table end cell blank end table close square brackets end cell row blank cell x equals negative 1 end cell row blank cell y equals 5 end cell end table

21)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 3 x plus y equals 3 end cell row blank cell 5 x plus 3 y equals 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 3 x plus y end cell row cell 5 x plus 3 y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 1 row 5 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator 9 minus 5 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 1 end cell row cell negative 5 end cell 3 end table end cell blank end table close square brackets equals 1 fourth open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 1 end cell row cell negative 5 end cell 3 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 5 over 4 end cell cell 3 over 4 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 5 over 4 end cell cell 3 over 4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 1 row 5 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 5 over 4 end cell cell 3 over 4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row 3 row 6 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell 3 over 4 end cell row cell 3 over 4 end cell end table end cell blank end table close square brackets end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell x equals 3 over 4 end cell row blank cell y equals 3 over 4 end cell end table

22)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell space of 1em table attributes columnspacing 1em end attributes row cell y minus x equals 5 end cell row cell 2 y minus 2 x equals 8 end cell end table end cell row blank cell negative x plus y equals 5 end cell row blank cell negative 2 x plus 2 y equals 8 end cell row blank cell open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative x plus y end cell row cell negative 2 x plus 2 y end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 5 row 8 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 1 row cell negative 2 end cell 2 end table end cell blank end table close square brackets open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 5 row 8 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 2 plus 2 end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets equals 1 over 0 open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 2 cell negative 1 end cell row 2 cell negative 1 end cell end table end cell blank end table close square brackets end cell end table

ليس لها حل.

23)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 4 x plus 2 y equals 6 end cell row blank cell 6 x minus 3 y equals 9 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 4 2 row 6 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row 6 row 9 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 12 minus 12 end fraction open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 6 end cell 4 end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 8 end cell cell 1 over 12 end cell row cell 1 fourth end cell cell negative 1 over 6 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 8 end cell cell 1 over 12 end cell row cell 1 fourth end cell cell negative 1 over 6 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 4 2 row 6 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell 1 over 8 end cell cell 1 over 12 end cell row cell 1 fourth end cell cell negative 1 over 6 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row 6 row 9 end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell 3 over 2 end cell row 0 end table end cell blank end table close square brackets space of 1em x equals 3 over 2 comma y equals 0 end cell end table

24)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 1.6 y minus 0.2 x equals 1 end cell row blank cell 0.4 y minus 0.1 x equals 0.5 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 0.2 end cell cell 1.6 end cell row cell negative 0.1 end cell cell 0.4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 1 row cell 0.5 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 0.2 right parenthesis left parenthesis 0.4 right parenthesis minus left parenthesis negative 0.1 right parenthesis left parenthesis 1.6 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0.4 end cell cell negative 1.6 end cell row cell 0.1 end cell cell negative 0.2 end cell end table end cell blank end table close square brackets equals fraction numerator 1 over denominator 0.08 end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell 0.4 end cell cell negative 1.6 end cell row cell 0.1 end cell cell negative 0.2 end cell end table end cell blank end table close square brackets end cell row blank cell space of 1em open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell fraction numerator 0.4 over denominator 0.08 end fraction end cell cell fraction numerator negative 1.6 over denominator 0.08 end fraction end cell row cell fraction numerator 0.1 over denominator 0.08 end fraction end cell cell fraction numerator negative 0.2 over denominator 0.08 end fraction end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 cell negative 20 end cell row cell 1.25 end cell cell negative 2.5 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 cell negative 20 end cell row cell 1.25 end cell cell negative 2.5 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 0.2 end cell cell 1.6 end cell row cell negative 0.1 end cell cell 0.4 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 5 cell negative 20 end cell row cell 1.25 end cell cell negative 2.5 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 1 row cell 0.5 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 1 plus 2 end cell cell 8 minus 8 end cell row cell negative 0.25 plus 0.25 end cell cell 2 minus 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 5 minus 10 end cell row cell 1.25 minus 1.25 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 5 end cell row 0 end table end cell blank end table close square brackets end cell end table

25)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell table attributes columnalign right columnspacing 1em end attributes row cell 4 y minus x equals negative 2 end cell row cell 3 y minus x equals 6 end cell end table end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 4 row cell negative 1 end cell 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 2 end cell row 6 end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 3 minus left parenthesis negative 4 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 end cell 4 row cell negative 1 end cell 3 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell negative 2 end cell row 6 end table end cell blank end table close square brackets end cell end table

open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign left columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnspacing 1em end attributes row cell negative 30 end cell row cell negative 8 end cell end table end cell blank end table close square brackets space of 1em x equals negative 30 comma y equals negative 8

26)

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell 2 y minus 4 x equals 3 end cell row blank cell 4 x minus 3 y equals negative 6 end cell end table

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 4 end cell 2 row 4 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 3 row cell negative 6 end cell end table end cell blank end table close square brackets end cell row blank cell A with _ below to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis negative 4 right parenthesis left parenthesis negative 3 right parenthesis minus left parenthesis 4 right parenthesis left parenthesis 2 right parenthesis end fraction open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell end table end cell blank end table close square brackets equals 1 fourth open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row cell negative 3 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center center columnspacing 1em end attributes row cell negative 4 end cell 2 row 4 cell negative 3 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign right right columnspacing 1em end attributes row cell negative 3 over 4 end cell cell negative 1 half end cell row cell negative 1 end cell cell negative 1 end cell end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row 3 row cell negative 6 end cell end table end cell blank end table close square brackets end cell row blank cell open square brackets table row cell table attributes columnalign left left columnspacing 1em end attributes row 1 0 row 0 1 end table end cell blank end table close square brackets times open square brackets table row cell table attributes columnspacing 1em end attributes row x row y end table end cell blank end table close square brackets equals open square brackets table row cell table attributes columnalign center columnspacing 1em end attributes row cell 3 over 4 end cell row 3 end table end cell blank end table close square brackets end cell row blank cell x equals 3 over 4 comma y equals 3 end cell end table