Pertanyaan

Tentukan M − 1 jika ( 6 a 5 a ) M = ( − 1 a − 9 5 a )

Tentukan $M^{- 1}$ jika $(6 a 5 a) M = (- 1 a - 9 5 a)$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh

M to the power of negative 1 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell 39 over 4 end cell cell 34 over 4 end cell row cell negative 7 over 4 end cell cell negative 3 over 2 end cell end table close parentheses end cell end table

Pembahasan

Ingatlah rumus invers dan sifat invers matriks berikut: 1. 2. 3. Berdasarkan rumus dan sifat tersebut, maka Selanjutnya ingat operasi perkalian matriks berikut: Sehingga, Jadi, diperoleh .

Ingatlah rumus invers dan sifat invers matriks berikut:

1. $A equals open parentheses table row a b row c d end table close parentheses rightwards arrow A to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses$

2. A X equals B rightwards arrow X equals A to the power of negative 1 end exponent B

3. X A equals B rightwards arrow X equals B A to the power of negative 1 end exponent

Berdasarkan rumus dan sifat tersebut, maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 6 5 row a a end table close parentheses M end cell equals cell open parentheses table row cell negative 1 end cell cell negative 9 end cell row a cell 5 a end cell end table close parentheses end cell row cell open parentheses table row 6 5 row a a end table close parentheses end cell equals cell open parentheses table row cell negative 1 end cell cell negative 9 end cell row a cell 5 a end cell end table close parentheses M to the power of negative 1 end exponent end cell row cell open parentheses table row cell negative 1 end cell cell negative 9 end cell row a cell 5 a end cell end table close parentheses to the power of negative 1 end exponent open parentheses table row 6 5 row a a end table close parentheses end cell equals cell M to the power of negative 1 end exponent end cell row cell M to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator negative 1 times 5 a minus left parenthesis negative 9 right parenthesis times a end fraction open parentheses table row cell 5 a end cell 9 row cell negative a end cell cell negative 1 end cell end table close parentheses open parentheses table row 6 5 row a a end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 5 a plus 9 a end fraction open parentheses table row cell 5 a end cell 9 row cell negative a end cell cell negative 1 end cell end table close parentheses open parentheses table row 6 5 row a a end table close parentheses end cell row blank blank blank end table$

Selanjutnya ingat operasi perkalian matriks berikut:

open parentheses table row a b row c d end table close parentheses open parentheses table row e f row g h end table close parentheses equals open parentheses table row cell a e plus b g end cell cell a f plus b h end cell row cell c e plus d g end cell cell c f plus d h end cell end table close parentheses

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row cell M to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator negative 5 a plus 9 a end fraction open parentheses table row cell 5 a end cell 9 row cell negative a end cell cell negative 1 end cell end table close parentheses open parentheses table row 6 5 row a a end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 a end fraction open parentheses table row cell 30 a plus 9 a end cell cell 25 a plus 9 a end cell row cell negative 6 a minus a end cell cell negative 5 a minus a end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 a end fraction open parentheses table row cell 39 a end cell cell 34 a end cell row cell negative 7 a end cell cell negative 6 a end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 39 a over denominator 4 a end fraction end cell cell fraction numerator 34 a over denominator 4 a end fraction end cell row cell fraction numerator negative 7 a over denominator 4 a end fraction end cell cell fraction numerator negative 6 a over denominator 4 a end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 39 over 4 end cell cell 34 over 4 end cell row cell negative 7 over 4 end cell cell negative 3 over 2 end cell end table close parentheses end cell end table$

Jadi, diperoleh .