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Diketahui matriks A = ( 4 3 ​ − 9 − 4 p ​ ) , B = ( 5 p 1 ​ − 5 3 ​ ) dan C = ( − 10 − 4 ​ 8 6 p ​ ) . Jika A − B = C − 1 , maka 2 p adalah ....

Diketahui matriks  dan . Jika  maka  adalah ....

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R. RGFLLIMA

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i, nilia adalah 1.

i, nilia  2 p adalah 1.

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Pembahasan

Operasi pengurangan pada matriks : Invers matriks C. Kesamaan matriks maka : Dari hasiil di ayas maka: Jadii, nilia adalah 1.

Operasi pengurangan pada matriks :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight A minus straight B end cell equals cell open parentheses table row 4 cell negative 9 end cell row 3 cell negative 4 straight p end cell end table close parentheses minus open parentheses table row cell 5 straight p end cell cell negative 5 end cell row 1 3 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 5 straight p end cell cell negative 9 plus 5 end cell row cell 3 minus 1 end cell cell negative 4 straight p minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 5 straight p end cell cell negative 4 end cell row 2 cell negative 4 straight p minus 3 end cell end table close parentheses end cell end table 

Invers matriks C.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight C to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator det space straight C end fraction Adj space straight C end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 10 right parenthesis times 6 straight p minus left parenthesis negative 4 right parenthesis times left parenthesis 8 right parenthesis end fraction open parentheses table row cell 6 straight p end cell cell negative 8 end cell row 4 cell negative 10 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 60 straight p plus 32 end fraction open parentheses table row cell 6 straight p end cell cell negative 8 end cell row 4 cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 6 straight p over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 8 over denominator negative 60 straight p plus 32 end fraction end cell row cell fraction numerator 4 over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 10 over denominator negative 60 straight p plus 32 end fraction end cell end table close parentheses end cell end table 

Kesamaan matriks A minus B equals C to the power of negative 1 end exponent comma maka :

open parentheses table row cell 4 minus 5 straight p end cell cell negative 4 end cell row 2 cell negative 4 straight p minus 3 end cell end table close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell fraction numerator 6 straight p over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 8 over denominator negative 60 straight p plus 32 end fraction end cell row cell fraction numerator 4 over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 10 over denominator negative 60 straight p plus 32 end fraction end cell end table close parentheses end cell end table

Dari hasiil di ayas maka:

table attributes columnalign right center left columnspacing 0px end attributes row 2 equals cell fraction numerator 4 over denominator negative 60 straight p plus 32 end fraction end cell row cell 2 left parenthesis negative 60 straight p plus 32 right parenthesis end cell equals 4 row cell negative 120 straight p plus 64 end cell equals 4 row cell negative 120 straight p end cell equals cell negative 60 end cell row straight p equals cell fraction numerator negative 60 over denominator negative 120 end fraction end cell row blank equals cell 1 half end cell row cell 2 straight p end cell equals 1 end table 

Jadii, nilia  2 p adalah 1.

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