Pertanyaan

Jika A T = ( 2 3 − 1 1 ) , A dan B memiliki invers, dan ( A B − 1 ) − 1 = ( 1 3 − 1 0 ) , maka nilai matriks sama dengan ...

Jika $A^{T} = (23 - 1 1)$ , $A$ dan $B$ memiliki invers, dan $(A B^{- 1})^{- 1} = (13 - 1 0)$ , maka nilai matriks sama dengan ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban tidak ada yang tepat.

Pembahasan

Transpose matriks , yaitu: Diketahui: , maka matriks yaitu: Ingatlah pada persamaan matriks , berlaku: Sehingga diperoleh perhitungannya adalah sebagai berikut: Maka nilai matriks sama dengan . Jadi, jawaban tidak ada yang tepat.

Transpose matriks A equals open parentheses table row a b row c d end table close parentheses , yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row a b row c d end table close parentheses end cell row cell A to the power of T end cell equals cell open parentheses table row a c row b d end table close parentheses end cell end table

Diketahui: A to the power of T equals open parentheses table row 2 cell negative 1 end cell row 3 1 end table close parentheses , maka matriks yaitu:

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

Ingatlah pada persamaan matriks, berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row cell A X end cell equals B row X equals cell A to the power of negative 1 end exponent times B end cell end table

Sehingga diperoleh perhitungannya adalah sebagai berikut:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses A B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row cell A to the power of negative 1 end exponent B end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row cell open parentheses table row 2 3 row cell negative 1 end cell 1 end table close parentheses to the power of negative 1 end exponent times B end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row cell fraction numerator 1 over denominator 2 open parentheses 1 close parentheses minus 3 open parentheses negative 1 close parentheses end fraction open parentheses table row 1 cell negative 3 end cell row 1 2 end table close parentheses times B end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row cell fraction numerator 1 over denominator 2 plus 3 end fraction open parentheses table row 1 cell negative 3 end cell row 1 2 end table close parentheses times B end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row cell 1 fifth open parentheses table row 1 cell negative 3 end cell row 1 2 end table close parentheses times B end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row cell open parentheses table row cell 1 fifth end cell cell negative 3 over 5 end cell row cell 1 fifth end cell cell 2 over 5 end cell end table close parentheses times B end cell equals cell open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row B equals cell open parentheses table row cell 1 fifth end cell cell negative 3 over 5 end cell row cell 1 fifth end cell cell 2 over 5 end cell end table close parentheses to the power of negative 1 end exponent times open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 fifth end style open parentheses begin display style 2 over 5 end style close parentheses minus open parentheses negative begin display style 3 over 5 end style close parentheses open parentheses begin display style 1 fifth end style close parentheses end fraction open parentheses table row cell 2 over 5 end cell cell 3 over 5 end cell row cell negative 1 fifth end cell cell 1 fifth end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator begin display style 2 over 25 end style plus begin display style 3 over 25 end style end fraction open parentheses table row cell 2 over 5 end cell cell 3 over 5 end cell row cell negative 1 fifth end cell cell 1 fifth end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator begin display style 5 over 25 end style end fraction open parentheses table row cell 2 over 5 end cell cell 3 over 5 end cell row cell negative 1 fifth end cell cell 1 fifth end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell 25 over 5 open parentheses table row cell 2 over 5 end cell cell 3 over 5 end cell row cell negative 1 fifth end cell cell 1 fifth end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell 5 open parentheses table row cell 2 over 5 end cell cell 3 over 5 end cell row cell negative 1 fifth end cell cell 1 fifth end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell open parentheses table row 2 3 row cell negative 1 end cell 1 end table close parentheses open parentheses table row 1 cell negative 1 end cell row 3 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 open parentheses 1 close parentheses plus 3 open parentheses 3 close parentheses end cell cell 2 open parentheses negative 1 close parentheses plus 3 open parentheses 0 close parentheses end cell row cell negative 1 left parenthesis 1 right parenthesis plus 1 left parenthesis 3 right parenthesis end cell cell negative 1 left parenthesis negative 1 right parenthesis plus 1 open parentheses 0 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus 9 end cell cell negative 2 plus 0 end cell row cell negative 1 plus 3 end cell cell 1 plus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row 11 cell negative 2 end cell row 2 1 end table close parentheses end cell end table end style$

Maka nilai matriks sama dengan open parentheses table row 11 cell negative 2 end cell row 2 1 end table close parentheses .

Jadi, jawaban tidak ada yang tepat.