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diketahui matriks dan jika dan adalah invers matri...

diketahui matriks p equals open parentheses table row 2 5 row 1 3 end table close parentheses dan Q equals open parentheses table row 5 4 row 1 1 end table close parentheses jika P to the power of negative 1 end exponent dan Q to the power of negative 1 end exponent adalah invers matriks Q, maka determinan matriks P to the power of negative 1 end exponent.Q to the power of negative 1 end exponent adalah....

  1. 223

  2. I

  3. -1

  4. -10

  5. -223

Jawaban:

Ingat sifat invers matriks berikut :

P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals left parenthesis Q P right parenthesis to the power of negative 1 end exponent

Maka,

P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals left parenthesis Q P right parenthesis to the power of negative 1 end exponent

P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals open square brackets open parentheses table row 5 4 row 1 1 end table close parentheses open parentheses table row 2 5 row 1 3 end table close parentheses close square brackets to the power of negative 1 end exponent

P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals open square brackets open parentheses table row 14 37 row 3 8 end table close parentheses close square brackets to the power of negative 1 end exponent

P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals fraction numerator 1 over denominator left parenthesis 14 right parenthesis left parenthesis 8 right parenthesis minus left parenthesis 3 right parenthesis left parenthesis 37 right parenthesis end fraction open parentheses table row 8 cell negative 37 end cell row cell negative 3 end cell 14 end table close parentheses

P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals 1 over 10 open parentheses table row 8 cell negative 37 end cell row cell negative 3 end cell 14 end table close parentheses

 

Sehingga,

D e t space P to the power of negative 1 end exponent Q to the power of negative 1 end exponent equals 1 over 10 left parenthesis 112 minus 111 right parenthesis equals 1 over 10.10 equals 1

Jawaban B

0

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