Roboguru

Diberikan matriks-matriks: Carilah matriks berordo yang memenuhi persamaan .

Diberikan matriks-matriks:

begin mathsize 14px style P equals open square brackets table row 2 0 row 1 3 end table close square brackets comma space Q equals open square brackets table row 16 2 row 1 cell negative 1 end cell end table close square brackets end style

Carilah matriks size 14px X berordo begin mathsize 14px style 2 cross times 2 end style yang memenuhi persamaan size 14px 2 size 14px X size 14px plus size 14px Q size 14px equals size 14px 3 size 14px P.

Jawaban:

Dengan menggunakan operasi perhitungan matriks dan kesamaan matriks, maka begin mathsize 14px style X end style dapat dicari dengan cara berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 X plus Q end cell equals cell 3 P end cell row cell 2 X end cell equals cell 3 P minus Q end cell row cell 2 X end cell equals cell 3 open square brackets table row 2 0 row 1 3 end table close square brackets minus open square brackets table row 16 2 row 1 cell negative 1 end cell end table close square brackets end cell row cell 2 X end cell equals cell open square brackets table row 6 0 row 3 9 end table close square brackets minus open square brackets table row 16 2 row 1 cell negative 1 end cell end table close square brackets end cell row cell 2 X end cell equals cell open square brackets table row cell negative 10 end cell cell negative 2 end cell row 2 10 end table close square brackets end cell row X equals cell open square brackets table row cell fraction numerator negative 10 over denominator 2 end fraction end cell cell fraction numerator negative 2 over denominator 2 end fraction end cell row cell 2 over 2 end cell cell 10 over 2 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 5 end cell cell negative 1 end cell row 1 5 end table close square brackets end cell end table end style

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank X end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell negative 5 end cell cell negative 1 end cell row 1 5 end table close square brackets end cell end table end style.

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