Pertanyaan

Tentukan invers matriks berikut. 1. Q = [ − 2 3 1 − 4 ]

Tentukan invers matriks berikut.

1. $Q = [- 2 3 1 - 4]$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

inver matriks atau adalah

inver matriks

atau

adalah

begin mathsize 14px style open square brackets table row cell negative 4 over 5 end cell cell negative 1 fifth end cell row cell negative 3 over 5 end cell cell negative 2 over 5 end cell end table close square brackets end style

Pembahasan

Diketahui matriks , maka: Jadi inver matriks atau adalah

Diketahui matriks , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Q to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator det space Q end fraction cross times Adj space Q end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 2 cross times left parenthesis negative 4 right parenthesis right parenthesis minus left parenthesis 3 cross times 1 right parenthesis end fraction open square brackets table row cell negative 4 end cell cell negative 1 end cell row cell negative 3 end cell cell negative 2 end cell end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator 8 minus 3 end fraction open square brackets table row cell negative 4 end cell cell negative 1 end cell row cell negative 3 end cell cell negative 2 end cell end table close square brackets end cell row blank equals cell 1 fifth open square brackets table row cell negative 4 end cell cell negative 1 end cell row cell negative 3 end cell cell negative 2 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 over 5 end cell cell negative 1 fifth end cell row cell negative 3 over 5 end cell cell negative 2 over 5 end cell end table close square brackets end cell end table end style$

Jadi inver matriks atau adalah begin mathsize 14px style open square brackets table row cell negative 4 over 5 end cell cell negative 1 fifth end cell row cell negative 3 over 5 end cell cell negative 2 over 5 end cell end table close square brackets end style