Pertanyaan

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 $A = (43 - 9 - 4 p)$ , $B = (5 p 1 - 5 3)$ dan $C = (- 10 - 4 8 6 p)$ . Jika $A - B = C^{- 1},$ maka $2 p$ adalah ....

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Jawaban terverifikasi

Jawaban

i, nilia adalah 1.

i, nilia

adalah 1.

Pembahasan

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

Operasi pengurangan pada matriks :

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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