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Hasil kali matriks A(50​−36​)=(−1035​30−27​). Matriks A adalah ...

Pertanyaan

Hasil kali matriks A open parentheses table row 5 cell negative 3 end cell row 0 6 end table close parentheses equals open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses. Matriks A adalah ...

  1. open parentheses table row cell negative 1 end cell cell negative 1 end cell row 4 7 end table close parentheses

  2. open parentheses table row cell negative 2 end cell 4 row 7 cell negative 1 end cell end table close parentheses

  3. open parentheses table row 4 cell negative 2 end cell row 7 cell negative 1 end cell end table close parentheses

  4. open parentheses table row 7 2 row cell negative 1 end cell 4 end table close parentheses

  5. open parentheses table row 7 2 row 4 cell negative 1 end cell end table close parentheses

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Persamaan matriks dengan A adalah matriks persegi yang mempunyai invers atau A to the power of negative 1 end exponent berlaku:

  • 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

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

Rumus perkalian dua buah matriks 2 cross times 2 yaitu:

open parentheses table row a b row c d end table close parentheses open parentheses table row p q row r s end table close parentheses equals open parentheses table row cell a times p plus b times r end cell cell a times q plus b times s end cell row cell c times p plus d times r end cell cell c times q plus d times s end cell end table close parentheses

Diperoleh penyelesaiannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell A open parentheses table row 5 cell negative 3 end cell row 0 6 end table close parentheses end cell equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses times open parentheses table row 5 cell negative 3 end cell row 0 6 end table close parentheses to the power of negative 1 end exponent end cell row A equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses times fraction numerator 1 over denominator 5 open parentheses 6 close parentheses minus open parentheses negative 3 close parentheses open parentheses 0 close parentheses end fraction open parentheses table row 6 3 row 0 5 end table close parentheses end cell row A equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses times fraction numerator 1 over denominator 30 minus 0 end fraction open parentheses table row 6 3 row 0 5 end table close parentheses end cell row A equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses times 1 over 30 open parentheses table row 6 3 row 0 5 end table close parentheses end cell row A equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses times open parentheses table row cell 6 over 30 end cell cell 3 over 30 end cell row cell 0 over 30 end cell cell 5 over 30 end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 10 end cell 30 row 35 cell negative 27 end cell end table close parentheses times open parentheses table row cell 1 fifth end cell cell 1 over 10 end cell row 0 cell 1 over 6 end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 10 open parentheses 1 fifth close parentheses plus 30 open parentheses 0 close parentheses end cell cell negative 10 open parentheses 1 over 10 close parentheses plus 30 open parentheses 1 over 6 close parentheses end cell row cell 35 open parentheses 1 fifth close parentheses plus open parentheses negative 27 close parentheses open parentheses 0 close parentheses end cell cell 35 open parentheses 1 over 10 close parentheses plus open parentheses negative 27 close parentheses open parentheses 1 over 6 close parentheses end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 2 plus 0 end cell cell negative 1 plus 5 end cell row cell 7 plus 0 end cell cell 35 over 10 minus 27 over 6 end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 2 end cell 4 row 7 cell fraction numerator 35 open parentheses 3 close parentheses over denominator 10 open parentheses 3 close parentheses end fraction minus fraction numerator 27 open parentheses 5 close parentheses over denominator 6 open parentheses 5 close parentheses end fraction end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 2 end cell 4 row 7 cell 105 over 30 minus 135 over 30 end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 2 end cell 4 row 7 cell negative 30 over 30 end cell end table close parentheses end cell row A equals cell open parentheses table row cell negative 2 end cell 4 row 7 cell negative 1 end cell end table close parentheses end cell end table

Matriks A adalah open parentheses table row cell negative 2 end cell 4 row 7 cell negative 1 end cell end table close parentheses.

Oleh karena itu, jawaban yang benar adalah B.

98

4.5 (2 rating)

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