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Diketahui matriks  dan . Matriks  yang memenuhi kesamaan  adalah...

Pertanyaan

Diketahui matriks A equals open parentheses table row 2 3 row 4 5 end table close parentheses dan B equals open parentheses table row 6 4 row 3 1 end table close parentheses. Matriks X yang memenuhi kesamaan A X equals B to the power of t adalah...

  1. open parentheses table row 18 12 row cell negative 16 end cell cell negative 10 end cell end table close parentheses 

  2. open parentheses table row 9 6 row cell negative 8 end cell cell negative 5 end cell end table close parentheses 

  3. open parentheses table row cell negative 9 end cell cell negative 6 end cell row 8 5 end table close parentheses 

  4. open parentheses table row 18 12 row 16 cell negative 10 end cell end table close parentheses 

  5. open parentheses table row cell negative 9 end cell 6 row cell negative 8 end cell 5 end table close parentheses 

Pembahasan Soal:

Menentukan B to the power of t

B to the power of t equals open parentheses table row 6 3 row 4 1 end table close parentheses

Menentukan determinan matriks A

equals 2 times 5 minus 3 times 4 equals 10 minus 12 equals negative 2 

Menentukan matriks A to the power of negative 1 end exponent

table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator negative 2 end fraction open parentheses table row 5 cell negative 3 end cell row cell negative 4 end cell 2 end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator negative 5 over denominator 2 end fraction end cell cell 3 over 2 end cell row 2 cell negative 1 end cell end table close parentheses end cell end table 

Menentukan matriks X

table attributes columnalign right center left columnspacing 0px end attributes row cell A X end cell equals cell B to the power of t end cell row X equals cell A to the power of negative 1 end exponent B to the power of t end cell row blank equals cell open parentheses table row cell fraction numerator negative 5 over denominator 2 end fraction end cell cell 3 over 2 end cell row 2 cell negative 1 end cell end table close parentheses open parentheses table row 6 3 row 4 1 end table close parentheses end cell row blank equals cell open parentheses table row cell left parenthesis fraction numerator negative 5 over denominator 2 end fraction right parenthesis times 6 plus 3 over 2 times 4 end cell cell left parenthesis fraction numerator negative 5 over denominator 2 end fraction right parenthesis times 3 plus 3 over 2 times 1 end cell row cell 2 times 6 plus left parenthesis negative 1 right parenthesis times 4 end cell cell 2 times 3 plus left parenthesis negative 1 right parenthesis times 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 15 plus 6 end cell cell fraction numerator negative 15 over denominator 2 end fraction plus 3 over 2 end cell row cell 12 minus 4 end cell cell 6 minus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 9 end cell cell negative 6 end cell row 8 5 end table close parentheses end cell end table  

Jadi, jawaban yang benar adalah C. 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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