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Matriks X berordo 2×2 yang memenuhi (13​24​)X=(42​31​) adalah ....

Pertanyaan

Matriks Error converting from MathML to accessible text. berordo size 14px 2 size 14px cross times size 14px 2 yang memenuhi begin mathsize 14px style open parentheses table row 1 2 row 3 4 end table close parentheses straight X equals open parentheses table row 4 3 row 2 1 end table close parentheses end style adalah ....

  1. begin mathsize 14px style open parentheses table row cell negative 6 end cell cell negative 5 end cell row 5 4 end table close parentheses end style 

  2. begin mathsize 14px style open parentheses table row 5 cell negative 6 end cell row 4 5 end table close parentheses end style 

  3. begin mathsize 14px style open parentheses table row cell negative 6 end cell cell negative 5 end cell row 4 5 end table close parentheses end style 

  4. begin mathsize 14px style open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses end style 

  5. begin mathsize 14px style open parentheses table row 12 10 row cell negative 10 end cell cell negative 8 end cell end table close parentheses end style 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jika diberikan persamaan matriks begin mathsize 14px style AX equals straight B end style. maka dapat ditentukan matriks begin mathsize 14px style straight X end style yang memenuhi persamaan matriks tersebut sebagai berikut.

begin mathsize 14px style straight X equals straight A to the power of negative 1 end exponent straight B end style

Berdasarkan informasi yang diberikan di atas, diketahui begin mathsize 14px style straight A equals open parentheses table row 1 2 row 3 4 end table close parentheses end style dan begin mathsize 14px style straight B equals open parentheses table row 4 3 row 2 1 end table close parentheses end style, sehingga dapat ditentukan matriks X sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row straight X equals cell straight A to the power of negative 1 end exponent straight B end cell row blank equals cell open parentheses table row cell table row 1 2 row 3 4 end table end cell end table close parentheses to the power of negative 1 end exponent times open parentheses table row 4 3 row 2 1 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 1 times 4 minus 2 times 3 end fraction times open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses times open parentheses table row 4 3 row 2 1 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 1 times 4 minus 2 times 3 end fraction times open parentheses table row cell 4 times 4 plus left parenthesis negative 2 right parenthesis times 2 end cell cell 4 times 3 plus left parenthesis negative 2 right parenthesis times 1 end cell row cell negative 3 times 4 plus 1 times 2 end cell cell negative 3 times 3 plus 1 times 1 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 minus 6 end fraction times open parentheses table row cell 16 minus 4 end cell cell 12 minus 2 end cell row cell negative 12 plus 2 end cell cell negative 9 plus 1 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 2 end fraction times open parentheses table row 12 10 row cell negative 10 end cell cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 12 over denominator negative 2 end fraction end cell cell fraction numerator 10 over denominator negative 2 end fraction end cell row cell fraction numerator negative 10 over denominator negative 2 end fraction end cell cell fraction numerator negative 8 over denominator negative 2 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell cell negative 5 end cell row 5 4 end table close parentheses end cell end table

Jadi, jawaban yang benar adalah A.

186

5.0 (2 rating)

Pertanyaan serupa

Diketahui matriks A=(20​−16​), C=(01​81​), dan D=(411​3−31​) Jika D=AB−C, tentukan matriks B.

125

5.0

Jawaban terverifikasi

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