Pertanyaan

Jika X matriks berordo 2 × 2 , tentukan matriks X yang memenuhi persamaan berikut! b. X [ 4 0 2 − 1 ] = [ 8 − 12 − 1 − 1 ]

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

b. $X [40 2 - 1] = [8 - 12 - 1 - 1]$

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Jawaban terverifikasi

Jawaban

matriks

Pembahasan

Jika , maka Matriks X tersebut dapat ditentukan sebagai berikut. Dengan demikian, matriks

Jika , 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.

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

Dengan demikian, matriks