Pertanyaan

Tentukan invers matriks berordo 3 × 3 di bawah ini dengan prinsip OBE . A = ⎝ ⎛ 3 − 1 1 − 1 1 0 1 0 1 ⎠ ⎞

Tentukan invers matriks berordo $3 \times 3$ di bawah ini dengan prinsip OBE.

$A = ⎝ ⎛ 3 - 1 1 - 1 10 101 ⎠ ⎞$

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

melalui prinsipOBEyang diuraikan di atas, invers matriks adalah

melalui prinsip OBE yang diuraikan di atas, invers matriks

adalah

A to the power of negative 1 end exponent equals open parentheses table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell negative 2 end cell 4 cell negative 6 end cell row cell negative 2 end cell 6 cell negative 6 end cell row 1 cell negative 3 end cell 6 end table end cell end table close parentheses

Pembahasan

Dengan prinsip OBE , maka: Jadimelalui prinsipOBEyang diuraikan di atas, invers matriks adalah

Dengan prinsip OBE, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space space space space space space space space open parentheses table row 3 cell negative 1 end cell 1 1 0 0 row cell negative 1 end cell 1 0 0 1 0 row 1 0 1 0 0 1 end table close parentheses table row cell bevelled 1 third space b subscript 1 end cell row blank row blank end table end cell row blank blank cell open parentheses table row 1 cell bevelled fraction numerator negative 1 over denominator 3 end fraction end cell cell bevelled 1 third end cell cell bevelled 1 third end cell 0 0 row cell negative 1 end cell 1 0 0 1 0 row 1 0 1 0 0 1 end table close parentheses table row blank row cell b subscript 2 plus b subscript 1 end cell row cell b subscript 3 minus b subscript 1 end cell end table end cell row blank blank cell space space space open parentheses table row 1 cell bevelled fraction numerator negative 1 over denominator 3 end fraction end cell cell bevelled 1 third end cell cell bevelled 1 third end cell 0 0 row 0 cell bevelled 2 over 3 end cell cell bevelled 1 third end cell cell bevelled 1 third end cell 1 0 row 0 cell bevelled 1 third end cell cell bevelled 2 over 3 end cell cell bevelled fraction numerator negative 1 over denominator 3 end fraction end cell 0 1 end table close parentheses table row blank row cell bevelled 3 over 2 space b subscript 2 end cell row blank end table end cell row blank blank cell space space space open parentheses table row 1 cell bevelled fraction numerator negative 1 over denominator 3 end fraction end cell cell bevelled 1 third end cell cell bevelled 1 third end cell 0 0 row 0 1 cell bevelled 1 half end cell cell bevelled 1 half end cell cell bevelled 3 over 2 end cell 0 row 0 cell bevelled 1 third end cell cell bevelled 2 over 3 end cell cell bevelled fraction numerator negative 1 over denominator 3 end fraction end cell 0 1 end table close parentheses table row cell space 3 b subscript 1 plus b subscript 2 end cell row blank row cell 3 b subscript 3 minus b subscript 2 end cell end table end cell row blank blank cell space space space space space space space space space space open parentheses table row 1 0 cell bevelled 3 over 2 end cell cell bevelled 3 over 2 end cell cell bevelled 3 over 2 end cell 0 row 0 1 cell bevelled 1 half end cell cell bevelled 1 half end cell cell bevelled 3 over 2 end cell 0 row 0 0 cell bevelled 1 half end cell cell bevelled 3 over 2 end cell cell bevelled fraction numerator negative 3 over denominator 2 end fraction end cell 3 end table close parentheses table row blank row blank row cell 2 cross times b subscript 3 end cell end table end cell row blank blank cell space space space space space space space space space space open parentheses table row 1 0 cell bevelled 3 over 2 end cell cell bevelled 3 over 2 end cell cell bevelled 3 over 2 end cell 0 row 0 1 cell bevelled 1 half end cell cell bevelled 1 half end cell cell bevelled 3 over 2 end cell 0 row 0 0 1 3 cell negative 3 end cell 6 end table close parentheses table row cell bevelled 2 over 3 space b subscript 1 minus b subscript 3 end cell row cell 2 b subscript 2 minus b subscript 3 end cell row blank end table end cell row blank blank cell space space space space space space space space space space space space space space open parentheses table row 1 0 0 cell negative 2 end cell 4 cell negative 6 end cell row 0 1 0 cell negative 2 end cell 6 cell negative 6 end cell row 0 0 1 1 cell negative 3 end cell 6 end table close parentheses table row blank row blank row blank end table end cell end table$

Jadi melalui prinsip OBE yang diuraikan di atas, invers matriks adalah