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Diketahui matriks A = [ 2 1 ​ − 1 3 ​ ] dan B = [ 4 7 ​ 1 − 2 ​ ] tentukanlah: b. B T ⋅ A − 1

Diketahui matriks  tentukanlah:

b.  

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H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

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adalah .

 begin mathsize 14px style B to the power of T times A to the power of negative 1 end exponent end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell 5 over 7 end cell cell 18 over 7 end cell row cell 5 over 7 end cell cell fraction numerator negative 3 over denominator 7 end fraction end cell end table close square brackets end cell end table.

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Pembahasan

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Ingat kembali aturan matriks dan transpose matrikssebagai berikut! Dengan aturan di atas, didapat perhitungan sebagai berikut. Dengan demikian, adalah .

Ingat kembali aturan matriks dan transpose matriks sebagai berikut!

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open square brackets table row a b row c d end table close square brackets end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator a d minus b 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 cell A to the power of T end cell equals cell open square brackets table row a c row b d end table close square brackets end cell end table

Dengan aturan di atas, didapat perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open square brackets table row 2 cell negative 1 end cell row 1 3 end table close square brackets end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 2 times 3 minus left parenthesis negative 1 right parenthesis times 1 end fraction open square brackets table row 3 1 row cell negative 1 end cell 2 end table close square brackets end cell row blank equals cell 1 over 7 open square brackets table row 3 1 row cell negative 1 end cell 2 end table close square brackets end cell row blank equals cell open square brackets table row cell 3 over 7 end cell cell 1 over 7 end cell row cell fraction numerator negative 1 over denominator 7 end fraction end cell cell 2 over 7 end cell end table close square brackets end cell row blank blank blank row B equals cell open square brackets table row 4 1 row 7 cell negative 2 end cell end table close square brackets end cell row cell B to the power of T end cell equals cell open square brackets table row 4 7 row 1 cell negative 2 end cell end table close square brackets end cell row blank blank blank row cell B to the power of T times A to the power of negative 1 end exponent end cell equals cell open square brackets table row 4 7 row 1 cell negative 2 end cell end table close square brackets times open square brackets table row cell 3 over 7 end cell cell 1 over 7 end cell row cell fraction numerator negative 1 over denominator 7 end fraction end cell cell 2 over 7 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator 12 minus 7 over denominator 7 end fraction end cell cell fraction numerator 4 plus 14 over denominator 7 end fraction end cell row cell fraction numerator 3 plus 2 over denominator 7 end fraction end cell cell fraction numerator 1 minus 4 over denominator 7 end fraction end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 5 over 7 end cell cell 18 over 7 end cell row cell 5 over 7 end cell cell fraction numerator negative 3 over denominator 7 end fraction end cell end table close square brackets end cell end table end style

Dengan demikian, begin mathsize 14px style B to the power of T times A to the power of negative 1 end exponent end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell 5 over 7 end cell cell 18 over 7 end cell row cell 5 over 7 end cell cell fraction numerator negative 3 over denominator 7 end fraction end cell end table close square brackets end cell end table.

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