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Jika PQ adalah matriks identitas dengan Q=(21​46​), maka matriks P= ...

Pertanyaan

Jika P Q adalah matriks identitas dengan Q equals open parentheses table row 2 4 row 1 6 end table close parentheses, maka matriks P equals ...

  1. open parentheses table row cell negative 1 fourth end cell 1 row cell 1 over 8 end cell cell negative 3 over 4 end cell end table close parentheses

  2. open parentheses table row cell negative 1 fourth end cell cell negative 1 half end cell row cell negative 1 over 8 end cell cell 3 over 4 end cell end table close parentheses

  3. open parentheses table row cell negative 3 over 4 end cell cell 1 half end cell row cell 1 over 8 end cell cell negative 1 fourth end cell end table close parentheses

  4. open parentheses table row cell 3 over 4 end cell cell negative 1 half end cell row cell negative 1 over 8 end cell cell 1 fourth end cell end table close parentheses

  5. open parentheses table row cell 1 fourth end cell cell negative 1 half end cell row cell negative 1 over 8 end cell cell 3 over 4 end cell end table close parentheses

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Diketahui:

P Q adalah matriks identitas, maka P Q equals open parentheses table row 1 0 row 0 1 end table close parentheses.

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

Sehingga diperoleh penyelesaiannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell P Q end cell equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell row cell P times open parentheses table row 2 4 row 1 6 end table close parentheses end cell equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell row P equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 2 4 row 1 6 end table close parentheses to the power of negative 1 end exponent end cell row P equals cell open parentheses table row 1 0 row 0 1 end table close parentheses times fraction numerator 1 over denominator 2 open parentheses 6 close parentheses minus 4 open parentheses 1 close parentheses end fraction open parentheses table row 6 cell negative 4 end cell row cell negative 1 end cell 2 end table close parentheses end cell row P equals cell open parentheses table row 1 0 row 0 1 end table close parentheses times fraction numerator 1 over denominator 12 minus 4 end fraction open parentheses table row 6 cell negative 4 end cell row cell negative 1 end cell 2 end table close parentheses end cell row P equals cell open parentheses table row 1 0 row 0 1 end table close parentheses times negative 1 over 8 open parentheses table row 6 cell negative 4 end cell row cell negative 1 end cell 2 end table close parentheses end cell row P equals cell open parentheses table row 1 0 row 0 1 end table close parentheses times open parentheses table row cell negative 1 over 8 open parentheses 6 close parentheses end cell cell negative 1 over 8 open parentheses negative 4 close parentheses end cell row cell negative 1 over 8 open parentheses negative 1 close parentheses end cell cell negative 1 over 8 open parentheses 2 close parentheses end cell end table close parentheses end cell row P equals cell open parentheses table row 1 0 row 0 1 end table close parentheses times open parentheses table row cell negative 3 over 4 end cell cell 1 half end cell row cell 1 over 8 end cell cell negative 1 fourth end cell end table close parentheses end cell row P equals cell open parentheses table row cell 1 open parentheses negative 3 over 4 close parentheses plus 0 open parentheses 1 over 8 close parentheses end cell cell 1 open parentheses 1 half close parentheses plus 0 open parentheses negative 1 fourth close parentheses end cell row cell 0 open parentheses negative 3 over 4 close parentheses plus 1 open parentheses 1 over 8 close parentheses end cell cell 0 open parentheses 1 half close parentheses plus 1 open parentheses negative 1 fourth close parentheses end cell end table close parentheses end cell row P equals cell open parentheses table row cell negative 3 over 4 plus 0 end cell cell 1 half plus 0 end cell row cell 0 plus 1 over 8 end cell cell 0 minus 1 fourth end cell end table close parentheses end cell row P equals cell open parentheses table row cell negative 3 over 4 end cell cell 1 half end cell row cell 1 over 8 end cell cell negative 1 fourth end cell end table close parentheses end cell end table

Maka matriks P equalsopen parentheses table row cell negative 3 over 4 end cell cell 1 half end cell row cell 1 over 8 end cell cell negative 1 fourth end cell end table close parentheses.

Oleh karena itu, jawaban yang benar adalah C.

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