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Jika , tentukan nilai  dan !

Jika begin mathsize 14px style open square brackets table row a b row 3 cell negative 2 end cell end table close square brackets times open square brackets table row 6 cell negative 5 end cell row 2 4 end table close square brackets equals open square brackets table row 12 cell negative 27 end cell row 14 cell negative 23 end cell end table close square brackets end style, tentukan nilai begin mathsize 14px style a end style dan begin mathsize 14px style b end style

Jawaban:

Perkalian antara dua matriks persegi dengan ordo sama adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row a b row 3 cell negative 2 end cell end table close square brackets times open square brackets table row 6 cell negative 5 end cell row 2 4 end table close square brackets end cell equals cell open square brackets table row cell a times 6 plus b times 2 end cell cell a times left parenthesis negative 5 right parenthesis plus b times 4 end cell row cell 3 times 6 plus left parenthesis negative 2 right parenthesis times 2 end cell cell 3 times left parenthesis negative 5 right parenthesis plus left parenthesis negative 2 right parenthesis times 4 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 6 a plus 2 b end cell cell negative 5 a plus 4 b end cell row 14 cell negative 23 end cell end table close square brackets end cell end table end style 

Dari hasil perkalian dua matriks persegi tersebut, diperoleh bahwa

begin mathsize 14px style open square brackets table row cell 6 a plus 2 b end cell cell negative 5 a plus 4 b end cell row 14 cell negative 23 end cell end table close square brackets equals open square brackets table row 12 cell negative 27 end cell row 14 cell negative 23 end cell end table close square brackets end style 

Sehingga,

begin mathsize 14px style 6 a plus 2 b equals 12 minus 5 a plus 4 b equals negative 27 end style 

Kemudian dilakukan substitusi untuk dua persamaan tersebut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 a plus 2 b end cell equals 12 row blank left right double arrow cell b equals fraction numerator 12 minus 6 a over denominator 2 end fraction end cell row blank equals cell 6 minus 3 a end cell end table end style 

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 5 a plus 4 left parenthesis 6 minus 3 a right parenthesis end cell equals cell negative 27 end cell row cell negative 5 a plus 24 minus 12 a end cell equals cell negative 27 end cell row cell negative 17 a end cell equals cell negative 51 end cell row a equals 3 end table end style 

Sedangkan nilai begin mathsize 14px style b end style yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row b equals cell 6 minus 3 a end cell row blank equals cell 6 minus 3 left parenthesis 3 right parenthesis end cell row blank equals cell 6 minus 9 end cell row blank equals cell negative 3 end cell end table end style 

Jadi, nilai begin mathsize 14px style a end style dan begin mathsize 14px style b end style berturut-turut adalah begin mathsize 14px style 3 end style dan begin mathsize 14px style negative 3 end style

  

 

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