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Pertanyaan

Diketahui A subscript x equals BB C equals D. Jika A equals open parentheses table row 1 2 row cell negative 3 end cell cell negative 5 end cell end table close parenthesesC equals open parentheses table row 3 2 row 1 1 end table close parentheses, dan D equals open parentheses table row 7 2 row 5 1 end table close parentheses, maka x adalah ...

  1. open parentheses table row 2 1 row 41 cell negative 19 end cell end table close parentheses

  2. open parentheses table row 33 54 row 19 31 end table close parentheses

  3. open parentheses table row cell negative 33 end cell 19 row 54 cell negative 31 end cell end table close parentheses

  4. open parentheses table row cell negative 33 end cell 54 row 19 cell negative 31 end cell end table close parentheses

  5. open parentheses table row cell negative 41 end cell cell negative 2 end cell row 19 1 end table close parentheses

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Pada persamaan matriks berlaku:

  • A X equals B

table attributes columnalign right center left columnspacing 0px end attributes row cell A X end cell equals B row cell A to the power of negative 1 end exponent A X end cell equals cell A to the power of negative 1 end exponent B end cell row cell I X end cell equals cell A to the power of negative 1 end exponent B end cell row X equals cell A to the power of negative 1 end exponent B end cell end table

  • X A equals B

table attributes columnalign right center left columnspacing 0px end attributes row cell X A end cell equals B row cell X A A to the power of negative 1 end exponent end cell equals cell B A to the power of negative 1 end exponent end cell row cell X I end cell equals cell B A to the power of negative 1 end exponent end cell row X equals cell B A to the power of negative 1 end exponent end cell end table

Tentukan terlebih dahulu matriks B dari persamaan B C equals D.

Diperoleh penyelesaiannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell B C end cell equals D row cell B C C to the power of negative 1 end exponent end cell equals cell D C to the power of negative 1 end exponent end cell row cell B I end cell equals cell D C to the power of negative 1 end exponent end cell row B equals cell D C to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row 7 2 row 5 1 end table close parentheses open parentheses table row 3 2 row 1 1 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row 7 2 row 5 1 end table close parentheses times fraction numerator 1 over denominator 3 open parentheses 1 close parentheses minus 2 open parentheses 1 close parentheses end fraction open parentheses table row 1 cell negative 2 end cell row cell negative 1 end cell 3 end table close parentheses end cell row blank equals cell open parentheses table row 7 2 row 5 1 end table close parentheses times fraction numerator 1 over denominator 3 minus 2 end fraction open parentheses table row 1 cell negative 2 end cell row cell negative 1 end cell 3 end table close parentheses end cell row blank equals cell open parentheses table row 7 2 row 5 1 end table close parentheses times 1 over 1 open parentheses table row 1 cell negative 2 end cell row cell negative 1 end cell 3 end table close parentheses end cell row blank equals cell open parentheses table row 7 2 row 5 1 end table close parentheses open parentheses table row 1 cell negative 2 end cell row cell negative 1 end cell 3 end table close parentheses end cell row blank equals cell open parentheses table row cell 7 open parentheses 1 close parentheses plus 2 open parentheses negative 1 close parentheses end cell cell 7 open parentheses negative 2 close parentheses plus 2 open parentheses 3 close parentheses end cell row cell 5 open parentheses 1 close parentheses plus 1 open parentheses negative 1 close parentheses end cell cell 5 open parentheses negative 2 close parentheses plus 1 open parentheses 3 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 7 minus 2 end cell cell negative 14 plus 6 end cell row cell 5 minus 1 end cell cell negative 10 plus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 cell negative 8 end cell row 4 cell negative 7 end cell end table close parentheses end cell row blank blank blank end table

Persamaan A subscript x equals B memiliki arti persamaan matriks A x equals B.

Kemudian dengan menggunakan sifat persamaan matriks, diperoleh matriks x yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell A x end cell equals B row cell A to the power of negative 1 end exponent A x end cell equals cell A to the power of negative 1 end exponent B end cell row cell I x end cell equals cell A to the power of negative 1 end exponent B end cell row x equals cell A to the power of negative 1 end exponent B end cell row blank equals cell open parentheses table row 1 2 row cell negative 3 end cell cell negative 5 end cell end table close parentheses to the power of negative 1 end exponent times open parentheses table row 5 cell negative 8 end cell row 4 cell negative 7 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 1 open parentheses negative 5 close parentheses minus 2 open parentheses negative 3 close parentheses end fraction open parentheses table row cell negative 5 end cell cell negative 2 end cell row 3 1 end table close parentheses open parentheses table row 5 cell negative 8 end cell row 4 cell negative 7 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 5 plus 6 end fraction open parentheses table row cell negative 5 open parentheses 5 close parentheses plus open parentheses negative 2 close parentheses open parentheses 4 close parentheses end cell cell negative 5 open parentheses negative 8 close parentheses plus open parentheses negative 2 close parentheses open parentheses negative 7 close parentheses end cell row cell 3 open parentheses 5 close parentheses plus 1 open parentheses 4 close parentheses end cell cell 3 open parentheses negative 8 close parentheses plus 1 open parentheses negative 7 close parentheses end cell end table close parentheses end cell row blank equals cell 1 times open parentheses table row cell negative 25 minus 8 end cell cell 40 plus 14 end cell row cell 15 plus 4 end cell cell negative 24 minus 7 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 33 end cell 54 row 19 cell negative 31 end cell end table close parentheses end cell end table

Maka x adalah open parentheses table row cell negative 33 end cell 54 row 19 cell negative 31 end cell end table close parentheses.

Oleh karena itu, jawaban yang benar adalah D.

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