Tentukan invers dari matriks A=[4523]!

Pertanyaan

Tentukan invers dari matriks $\style{font-size:14px}{A=\begin{bmatrix}4&2\\5&3\end{bmatrix}}$ !

R. Almira

Master Teacher

Mahasiswa/Alumni Universitas Pertamina

Jawaban terverifikasi

Jawaban

invers dari matriks begin mathsize 14px style A end style

adalah $begin mathsize 14px style A to the power of negative 1 end exponent equals open square brackets table row cell bevelled 3 over 2 end cell cell negative 1 end cell row cell bevelled fraction numerator negative 5 over denominator 2 end fraction end cell 2 end table close square brackets end style$ .

Pembahasan

Suatu matriks begin mathsize 14px style A equals open square brackets table row a b row c d end table close square brackets end style , dapat dicari inversnya begin mathsize 14px style open parentheses A to the power of negative 1 end exponent close parentheses end style dengan menggunakan rumus berikut:

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Invers dari matriks begin mathsize 14px style 2 cross times 2 end style pada soal adalah sebagai berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator det space A end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator a times d minus b times c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator 4 times 3 minus 5 times 2 end fraction open square brackets table row 3 cell negative 2 end cell row cell negative 5 end cell 4 end table close square brackets end cell row blank equals cell 1 half open square brackets table row 3 cell negative 2 end cell row cell negative 5 end cell 4 end table close square brackets end cell row blank equals cell open square brackets table row cell bevelled 3 over 2 end cell cell negative 1 end cell row cell bevelled fraction numerator negative 5 over denominator 2 end fraction end cell 2 end table close square brackets end cell end table end style$

Jadi, invers dari matriks begin mathsize 14px style A end style adalah $begin mathsize 14px style A to the power of negative 1 end exponent equals open square brackets table row cell bevelled 3 over 2 end cell cell negative 1 end cell row cell bevelled fraction numerator negative 5 over denominator 2 end fraction end cell 2 end table close square brackets end style$ .

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