Pertanyaan

Diketahui matriks A = [ 2 1 − 1 3 ] dan B = [ 4 7 1 − 2 ] tentukanlah: a. 2 A ⋅ B − 1

Diketahui matriks $A = [21 - 1 3] dan B = [47 1 - 2]$ tentukanlah:

a. $2 A \cdot B^{- 1}$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari 2 A times B to the power of negative 1 end exponent

adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell fraction numerator negative 2 over denominator 5 end fraction end cell cell 4 over 5 end cell row cell 46 over 15 end cell cell fraction numerator negative 22 over denominator 15 end fraction end cell end table close square brackets end cell end table$ .

Pembahasan

Invers matriks adalah kebalikan (invers) dari sebuah matriks yang apabila matriks tersebut dikalikan dengan inversnya, akan menjadi matriks identitas. Invers matriks dapat ditentukan dengan: Sehingga, Dengan demikian, nilai dari adalah .

Invers matriks adalah kebalikan (invers) dari sebuah matriks yang apabila matriks tersebut dikalikan dengan inversnya, akan menjadi matriks identitas.

Invers matriks 2 cross times 2 dapat ditentukan dengan:

$table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open square brackets table row a b row c d end table close square brackets end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets end cell end table$

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row B equals cell open square brackets table row 4 1 row 7 cell negative 2 end cell end table close square brackets end cell row cell B to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 4 times left parenthesis negative 2 right parenthesis minus 1 times 7 end fraction open square brackets table row cell negative 2 end cell cell negative 1 end cell row cell negative 7 end cell 4 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator negative 15 end fraction open square brackets table row cell negative 2 end cell cell negative 1 end cell row cell negative 7 end cell 4 end table close square brackets end cell row blank equals cell open square brackets table row cell 2 over 15 end cell cell 1 over 15 end cell row cell 7 over 15 end cell cell negative 4 over 15 end cell end table close square brackets end cell row blank blank blank row cell 2 A times B to the power of negative 1 end exponent end cell equals cell 2 open square brackets table row 2 cell negative 1 end cell row 1 3 end table close square brackets times open square brackets table row cell 2 over 15 end cell cell 1 over 15 end cell row cell 7 over 15 end cell cell negative 4 over 15 end cell end table close square brackets end cell row blank equals cell open square brackets table row 4 cell negative 2 end cell row 2 6 end table close square brackets open square brackets table row cell 2 over 15 end cell cell 1 over 15 end cell row cell 7 over 15 end cell cell negative 4 over 15 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator 8 minus 14 over denominator 15 end fraction end cell cell fraction numerator 4 plus 8 over denominator 15 end fraction end cell row cell fraction numerator 4 plus 42 over denominator 15 end fraction end cell cell fraction numerator 2 minus 24 over denominator 15 end fraction end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator negative 2 over denominator 5 end fraction end cell cell 4 over 5 end cell row cell 46 over 15 end cell cell fraction numerator negative 22 over denominator 15 end fraction end cell end table close square brackets end cell end table$

Dengan demikian, nilai dari 2 A times B to the power of negative 1 end exponent adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell fraction numerator negative 2 over denominator 5 end fraction end cell cell 4 over 5 end cell row cell 46 over 15 end cell cell fraction numerator negative 22 over denominator 15 end fraction end cell end table close square brackets end cell end table$ .