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Jika matriks  invers dari matriks . Carilah nilai ...

Jika matriks begin mathsize 14px style A equals open square brackets table row 1 cell negative 1 third end cell row cell negative 2 end cell 1 end table close square brackets end style invers dari matriks begin mathsize 14px style B equals open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets end style. Carilah nilai dari begin mathsize 14px style x end style dan begin mathsize 14px style y end style!

Jawaban:

Jika begin mathsize 14px style A equals open parentheses table row a b row c d end table close parentheses end style, maka begin mathsize 14px 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

Invers dari matriks A dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 1 minus open parentheses begin display style 2 over 3 end style close parentheses end fraction open square brackets table row 1 cell 1 third end cell row 2 1 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 third end style end fraction open square brackets table row 1 cell 1 third end cell row 2 1 end table close square brackets end cell row blank equals cell 3 open square brackets table row 1 cell 1 third end cell row 2 1 end table close square brackets end cell row blank equals cell open square brackets table row 3 1 row 6 3 end table close square brackets end cell end table end style

Dapat ditentukan persamaan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of negative 1 end exponent end cell equals B row cell open square brackets table row 3 1 row 6 3 end table close square brackets end cell equals cell open square brackets table row cell x plus 4 end cell 1 row 6 cell 2 x plus y end cell end table close square brackets end cell end table end style

begin mathsize 14px style 3 equals x plus 4 rightwards arrow x equals negative 1 3 equals 2 x plus y equals negative 2 plus y space rightwards arrow y equals 5 end style

Dengan demikian, nilai begin mathsize 14px style x equals negative 1 end style dan begin mathsize 14px style y equals 5 end style 

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