Pertanyaan

Jika X matriks berordo 2 × 2 , tentukan matriks X yang memenuhi persamaan berikut! a. [ 1 − 1 2 0 ] X = [ 1 4 5 − 1 ]

Jika X matriks berordo $2 \times 2$ , tentukan matriks X yang memenuhi persamaan berikut!

a. $[1 - 1 20] X = [14 5 - 1]$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

matriks

Pembahasan

Ingat kembali: dan Pertama kita tentukan invers dari matriks Matriks Sehingga matriks X dapat diperioleh: Dengan demikian, matriks

Ingat kembali:

A equals open parentheses table row a b row c d end table close parentheses rightwards arrow $begin mathsize 14px style A to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses end style$

dan

begin mathsize 14px style 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 B end cell end table end style

Pertama kita tentukan invers dari matriks Matriks open square brackets table row 1 2 row cell negative 1 end cell 0 end table close square brackets

$table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row 1 2 row cell negative 1 end cell 0 end table close square brackets to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 0 minus open parentheses negative 2 close parentheses end fraction open square brackets table row 0 cell negative 2 end cell row 1 1 end table close square brackets end cell row blank blank blank row blank equals cell 1 half open square brackets table row 0 cell negative 2 end cell row 1 1 end table close square brackets end cell row blank equals cell open square brackets table row 0 cell negative 1 end cell row cell 1 half end cell cell 1 half end cell end table close square brackets end cell end table$

Sehingga matriks X dapat diperioleh:

Dengan demikian, matriks begin mathsize 14px style X equals open square brackets table row cell negative 4 end cell 1 row cell 5 over 2 end cell 2 end table close square brackets end style