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Jika P = dan = dengan menyatakan invers matriks P, maka x + y = ...

Jika P = begin mathsize 12px style open parentheses table row 1 2 row 1 3 end table close parentheses end style dan begin mathsize 12px style open parentheses table row x y row cell negative z end cell z end table close parentheses end stylebegin mathsize 12px style 2 P to the power of negative 1 end exponent end style dengan size 12px P to the power of size 12px minus size 12px 1 end exponent menyatakan invers matriks P, maka x + y = ...

  1. 0

  2. 1

  3. 2

  4. 3

  5. 4

Jawaban:

Perhatikan sifat fungsi matriks

Jika matriks A = begin mathsize 12px style open parentheses table row a b row c d end table close parentheses end style, maka invers matriks A dirumuskan sebagai:

begin mathsize 12px style A to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b 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 style

 

Selesaikan persamaan

Diketahui nilai P = begin mathsize 12px style open parentheses table row 1 2 row 1 3 end table close parentheses end style, maka:

begin mathsize 12px style P to the power of negative 1 end exponent equals fraction numerator 1 over denominator 1.3 minus 2.1 end fraction open parentheses table row 3 cell negative 2 end cell row cell negative 1 end cell 1 end table close parentheses  P to the power of negative 1 end exponent equals fraction numerator 1 over denominator 3 minus 2 end fraction open parentheses table row 3 cell negative 2 end cell row cell negative 1 end cell 1 end table close parentheses  P to the power of negative 1 end exponent equals open parentheses table row 3 cell negative 2 end cell row cell negative 1 end cell 1 end table close parentheses  open parentheses table row x y row cell negative z end cell z end table close parentheses equals 2 P to the power of negative 1 end exponent end style

 

Tentukan nilainya

begin mathsize 12px style open parentheses table row x y row cell negative z end cell z end table close parentheses equals 2 open parentheses table row 3 cell negative 2 end cell row cell negative 1 end cell 1 end table close parentheses end style

Maka dapat diketahui nilai x = 6 dan y = - 4

Ditanya nilai x + y = 6 - 4 = 2 

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