Roboguru

Jika X matriks berordo , tentukan matriks X yang memenuhi persamaan berikut! b.

Pertanyaan

Jika X matriks berordo begin mathsize 14px style 2 cross times 2 end style, tentukan matriks X yang memenuhi persamaan berikut!

b. begin mathsize 14px style X open square brackets table row 4 2 row 0 cell negative 1 end cell end table close square brackets equals open square brackets table row 8 cell negative 1 end cell row cell negative 12 end cell cell negative 1 end cell end table close square brackets end style 

Pembahasan Soal:

Jika begin mathsize 14px style A equals open parentheses table row a b row c d end table close parentheses end style, maka 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 comma space a d minus b c not equal to 0

Matriks X tersebut dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell X A end cell equals B row X equals cell B times A to the power of negative 1 end exponent end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell X open square brackets table row 4 2 row 0 cell negative 1 end cell end table close square brackets end cell equals cell open square brackets table row 8 cell negative 1 end cell row cell negative 12 end cell cell negative 1 end cell end table close square brackets end cell row X equals cell open square brackets table row 8 cell negative 1 end cell row cell negative 12 end cell cell negative 1 end cell end table close square brackets times fraction numerator 1 over denominator open parentheses negative 4 minus 0 close parentheses end fraction open square brackets table row cell negative 1 end cell cell negative 2 end cell row 0 4 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator negative 4 end fraction open square brackets table row 8 cell negative 1 end cell row cell negative 12 end cell cell negative 1 end cell end table close square brackets open square brackets table row cell negative 1 end cell cell negative 2 end cell row 0 4 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator negative 4 end fraction open square brackets table row cell negative 8 end cell cell negative 20 end cell row 12 20 end table close square brackets end cell row blank equals cell open square brackets table row 2 5 row cell negative 3 end cell cell negative 5 end cell end table close square brackets end cell end table end style

Dengan demikian, matriks begin mathsize 14px style X equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row 2 5 row cell negative 3 end cell cell negative 5 end cell end table close square brackets end cell end table end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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