Pertanyaan

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

Diketahui matriks $A = [21 - 1 3] dan B = [47 1 - 2]$ tentukanlah:

b. $B^{T} \cdot A^{- 1}$

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Habis dalam

Klaim

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

adalah .

begin mathsize 14px style B to the power of T times A to the power of negative 1 end exponent end style

adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell 5 over 7 end cell cell 18 over 7 end cell row cell 5 over 7 end cell cell fraction numerator negative 3 over denominator 7 end fraction end cell end table close square brackets end cell end table$ .

Pembahasan

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 $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell 5 over 7 end cell cell 18 over 7 end cell row cell 5 over 7 end cell cell fraction numerator negative 3 over denominator 7 end fraction end cell end table close square brackets end cell end table$ .