Pertanyaan

Tentukan ( A B ) − 1 dan ( B A ) − 1 jika ada untuk informasi matriks di bawah ini. A = ⎝ ⎛ 2 1 − 3 3 3 − 2 − 1 5 2 ⎠ ⎞ dan B = ⎝ ⎛ 4 5 2 − 2 1 − 4 − 3 2 1 ⎠ ⎞

Tentukan $(A B)^{- 1}$ dan $(B A)^{- 1}$ jika ada untuk informasi matriks di bawah ini.

$A = ⎝ ⎛ 21 - 3 33 - 2 - 1 52 ⎠ ⎞$ dan $B = ⎝ ⎛ 452 - 2 1 - 4 - 3 21 ⎠ ⎞$

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

invers matriks adalah dan invers matriks adalah

invers matriks A B

adalah

open parentheses A B close parentheses to the power of negative 1 end exponent equals open parentheses table row cell 101 over 2704 end cell cell 17 over 2704 end cell cell negative 5 over 2704 end cell row cell 347 over 2704 end cell cell negative 129 over 2704 end cell cell 197 over 2704 end cell row cell 229 over 1352 end cell cell 15 over 1352 end cell cell 243 over 1352 end cell end table close parentheses

dan invers matriks B A

adalah $left parenthesis B A right parenthesis to the power of negative 1 end exponent equals open parentheses table row cell fraction numerator 31 over denominator 338 end fraction end cell cell negative fraction numerator 25 over denominator 169 end fraction end cell cell negative fraction numerator 41 over denominator 338 end fraction end cell row cell negative fraction numerator 11 over denominator 338 end fraction end cell cell fraction numerator 45 over denominator 338 end fraction end cell cell fraction numerator 10 over denominator 169 end fraction end cell row cell negative fraction numerator 1 over denominator 1352 end fraction end cell cell negative fraction numerator 21 over denominator 676 end fraction end cell cell fraction numerator 75 over denominator 1352 end fraction end cell end table close parentheses$

Pembahasan

dan ,maka: Melalui ekspansi kofaktor-minor, didapat: Melalui ekspansi kofaktor-minor, didapat: Jadi, invers matriks adalah dan invers matriks adalah

begin mathsize 14px style A equals open parentheses table row 2 3 cell negative 1 end cell row 1 3 5 row cell negative 3 end cell cell negative 2 end cell 2 end table close parentheses end style dan begin mathsize 14px style B equals open parentheses table row 4 cell negative 2 end cell cell negative 3 end cell row 5 1 2 row 2 cell negative 4 end cell 1 end table close parentheses end style ,maka:

A B equals open parentheses table row 21 3 cell negative 1 end cell row 29 cell negative 19 end cell 8 row cell negative 18 end cell cell negative 4 end cell 7 end table close parentheses

Melalui ekspansi kofaktor-minor, didapat:

B A equals open parentheses table row 15 12 cell negative 20 end cell row 5 14 4 row cell negative 3 end cell cell negative 8 end cell cell negative 20 end cell end table close parentheses

Melalui ekspansi kofaktor-minor, didapat:

$left parenthesis B A right parenthesis to the power of negative 1 end exponent equals open parentheses table row cell fraction numerator 31 over denominator 338 end fraction end cell cell negative fraction numerator 25 over denominator 169 end fraction end cell cell negative fraction numerator 41 over denominator 338 end fraction end cell row cell negative fraction numerator 11 over denominator 338 end fraction end cell cell fraction numerator 45 over denominator 338 end fraction end cell cell fraction numerator 10 over denominator 169 end fraction end cell row cell negative fraction numerator 1 over denominator 1352 end fraction end cell cell negative fraction numerator 21 over denominator 676 end fraction end cell cell fraction numerator 75 over denominator 1352 end fraction end cell end table close parentheses$

Jadi, invers matriks adalah dan invers matriks adalah $left parenthesis B A right parenthesis to the power of negative 1 end exponent equals open parentheses table row cell fraction numerator 31 over denominator 338 end fraction end cell cell negative fraction numerator 25 over denominator 169 end fraction end cell cell negative fraction numerator 41 over denominator 338 end fraction end cell row cell negative fraction numerator 11 over denominator 338 end fraction end cell cell fraction numerator 45 over denominator 338 end fraction end cell cell fraction numerator 10 over denominator 169 end fraction end cell row cell negative fraction numerator 1 over denominator 1352 end fraction end cell cell negative fraction numerator 21 over denominator 676 end fraction end cell cell fraction numerator 75 over denominator 1352 end fraction end cell end table close parentheses$

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