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Pertanyaan

Jika invers P adalah P − 1 = 5 1 ​ ( − 1 2 ​ − 4 3 ​ ) , maka P ⋅ ( x 1 ​ 1 y ​ ) = ...

Jika invers  adalah , maka  ...

  1. open parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell negative 2 x minus 1 end cell cell negative 2 minus y end cell end table close parentheses

  2. open parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell 2 x minus 1 end cell cell 2 minus y end cell end table close parentheses

  3. open parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell 2 x plus 1 end cell cell negative 2 minus y end cell end table close parentheses

  4. open parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell negative 2 x minus 1 end cell cell 2 minus y end cell end table close parentheses

  5. open parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell negative 2 x plus 1 end cell cell negative 2 plus y end cell end table close parentheses

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S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

jawaban yang benar adalah A.

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Pembahasan

Rumus invers matriks yaitu: Sifat invers matriks yaitu: Diperoleh penyelesaiannya yaitu: Maka . Oleh karena itu, jawaban yang benar adalah A.

Rumus invers matriks 2 cross times 2 yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row a b row c d end table close parentheses end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator a times d minus b times c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses end cell end table

Sifat invers matriks yaitu:

  • A A to the power of negative 1 end exponent equals A to the power of negative 1 end exponent A equals I
  • open parentheses A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent equals A

Diperoleh penyelesaiannya yaitu:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell P times open parentheses table row x 1 row 1 y end table close parentheses end cell equals cell open parentheses P to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times open parentheses table row x 1 row 1 y end table close parentheses end cell row blank equals cell open parentheses 1 fifth open parentheses table row cell negative 1 end cell cell negative 4 end cell row 2 3 end table close parentheses close parentheses to the power of negative 1 end exponent times open parentheses table row x 1 row 1 y end table close parentheses end cell row blank equals cell open parentheses table row cell 1 fifth open parentheses negative 1 close parentheses end cell cell 1 fifth open parentheses negative 4 close parentheses end cell row cell 1 fifth open parentheses 2 close parentheses end cell cell 1 fifth open parentheses 3 close parentheses end cell end table close parentheses to the power of negative 1 end exponent times open parentheses table row x 1 row 1 y end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 fifth end cell cell negative 4 over 5 end cell row cell 2 over 5 end cell cell 3 over 5 end cell end table close parentheses to the power of negative 1 end exponent times open parentheses table row x 1 row 1 y end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 1 fifth end style open parentheses begin display style 3 over 5 end style close parentheses minus open parentheses negative begin display style 4 over 5 end style close parentheses open parentheses begin display style 2 over 5 end style close parentheses end fraction open parentheses table row cell 3 over 5 end cell cell 4 over 5 end cell row cell negative 2 over 5 end cell cell negative 1 fifth end cell end table close parentheses times open parentheses table row x 1 row 1 y end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 3 over 25 end style plus begin display style 8 over 25 end style end fraction open parentheses table row cell 3 over 5 open parentheses x close parentheses plus 4 over 5 open parentheses 1 close parentheses end cell cell 3 over 5 open parentheses 1 close parentheses plus 4 over 5 open parentheses y close parentheses end cell row cell negative 2 over 5 open parentheses x close parentheses plus open parentheses negative 1 fifth close parentheses open parentheses 1 close parentheses end cell cell negative 2 over 5 open parentheses 1 close parentheses plus open parentheses negative 1 fifth close parentheses open parentheses y close parentheses end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator begin display style 5 over 25 end style end fraction open parentheses table row cell 3 over 5 x plus 4 over 5 end cell cell 3 over 5 plus 4 over 5 y end cell row cell negative 2 over 5 x minus 1 fifth end cell cell negative 2 over 5 minus 1 fifth y end cell end table close parentheses end cell row blank equals cell 1 times 25 over 5 open parentheses table row cell 3 over 5 x plus 4 over 5 end cell cell 3 over 5 plus 4 over 5 y end cell row cell negative 2 over 5 x minus 1 fifth end cell cell negative 2 over 5 minus 1 fifth y end cell end table close parentheses end cell row blank equals cell 5 times open parentheses table row cell 3 over 5 x plus 4 over 5 end cell cell 3 over 5 plus 4 over 5 y end cell row cell negative 2 over 5 x minus 1 fifth end cell cell negative 2 over 5 minus 1 fifth y end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell negative 2 x minus 1 end cell cell negative 2 minus y end cell end table close parentheses end cell end table end style

Maka P times open parentheses table row x 1 row 1 y end table close parentheses equalsopen parentheses table row cell 3 x plus 4 end cell cell 3 plus 4 y end cell row cell negative 2 x minus 1 end cell cell negative 2 minus y end cell end table close parentheses.

Oleh karena itu, jawaban yang benar adalah A.

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Pengertian Matriks

Operasi Hitung Matriks

Invers Matriks

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