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Diketahui matriks . Jika  invers matriks  dan  adalah invers matriks , maka deteminan matriks  adalah ...

Pertanyaan

Diketahui matriks A equals open parentheses table row 1 cell negative 1 end cell row 5 cell negative 4 end cell end table close parentheses comma thin space B equals open parentheses table row 7 3 row 2 1 end table close parentheses. Jika A to the power of negative 1 end exponent invers matriks A dan B to the power of negative 1 end exponent adalah invers matriks B, maka deteminan matriks B to the power of negative 1 end exponent A to the power of negative 1 end exponent adalah ...

  1. negative 20 

  2. negative 10 

  3. negative 1 

  4. 1 

  5. 10 

Pembahasan Soal:

Diketahui:

A equals open parentheses table row 1 cell negative 1 end cell row 5 cell negative 4 end cell end table close parentheses comma thin space B equals open parentheses table row 7 3 row 2 1 end table close parentheses

Mencari invers matriks A:

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 open parentheses table row 1 cell negative 1 end cell row 5 cell negative 4 end cell end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator det open parentheses table row 1 cell negative 1 end cell row 5 cell negative 4 end cell end table close parentheses end fraction open parentheses table row cell negative 4 end cell cell negative open parentheses negative 1 close parentheses end cell row cell negative 5 end cell 1 end table close parentheses end cell row blank equals cell 1 over 1 open parentheses table row cell negative 4 end cell cell negative open parentheses negative 1 close parentheses end cell row cell negative 5 end cell 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell 1 row cell negative 5 end cell 1 end table close parentheses end cell end table 

Mencari invers matriks B:

table attributes columnalign right center left columnspacing 0px end attributes row cell B to the power of negative 1 end exponent end cell equals cell open parentheses table row 7 3 row 2 1 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator det open parentheses table row 7 3 row 2 1 end table close parentheses end fraction open parentheses table row 1 cell negative 3 end cell row cell negative 2 end cell 7 end table close parentheses end cell row blank equals cell 1 over 1 open parentheses table row 1 cell negative 3 end cell row cell negative 2 end cell 7 end table close parentheses end cell row blank equals cell open parentheses table row 1 cell negative 3 end cell row cell negative 2 end cell 7 end table close parentheses end cell end table 

Mencari determinan matriks B to the power of negative 1 end exponent A to the power of negative 1 end exponent:

det open parentheses open parentheses table row 1 cell negative 3 end cell row cell negative 2 end cell 7 end table close parentheses open parentheses table row cell negative 4 end cell 1 row cell negative 5 end cell 1 end table close parentheses close parentheses equals det open parentheses table row 11 cell negative 2 end cell row cell negative 27 end cell 5 end table close parentheses equals 11 times 5 minus open parentheses negative 2 close parentheses open parentheses negative 27 close parentheses equals 1  

Jadi, determinan matriks B to the power of negative 1 end exponent A to the power of negative 1 end exponent adalah 1.

Dengan demikian, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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