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Matriks  dan . Supaya dipenuhi , dengan  menyataka...

Matriks begin mathsize 14px style straight A equals open square brackets table row straight a 4 row cell 2 straight b end cell cell 3 straight c end cell end table close square brackets end style dan begin mathsize 14px style straight B equals open square brackets table row cell 2 straight c minus 3 straight b end cell cell 2 straight a plus 1 end cell row straight a cell straight b plus 7 end cell end table close square brackets end style. Supaya dipenuhi begin mathsize 14px style straight A equals 2 straight B to the power of straight t end style, dengan begin mathsize 14px style straight B to the power of straight t end style menyatakan matriks transpos dari B maka nilai begin mathsize 14px style c equals horizontal ellipsis end style 

  1. 2space 

  2. 3space 

  3. 5space 

  4. 8space 

  5. 10space 

Jawaban:

begin mathsize 14px style straight A equals open square brackets table row a 4 row cell 2 b end cell cell 3 c end cell end table close square brackets end style dan begin mathsize 14px style straight B equals open square brackets table row cell 2 c minus 3 b end cell cell 2 a plus 1 end cell row a cell b plus 7 end cell end table close square brackets end style. Supaya dipenuhi begin mathsize 14px style straight A equals 2 straight B to the power of straight t end style maka perhatikan perhitungan di bawah ini.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell 2 straight B to the power of straight t end cell row cell open square brackets table row a 4 row cell 2 b end cell cell 3 c end cell end table close square brackets end cell equals cell 2 open square brackets table row cell 2 c minus 3 b end cell cell 2 a plus 1 end cell row a cell b plus 7 end cell end table close square brackets to the power of t end cell row cell open square brackets table row a 4 row cell 2 b end cell cell 3 c end cell end table close square brackets end cell equals cell 2 open square brackets table row cell 2 c minus 3 b end cell a row cell 2 a plus 1 end cell cell b plus 7 end cell end table close square brackets end cell row cell open square brackets table row a 4 row cell 2 b end cell cell 3 c end cell end table close square brackets end cell equals cell open square brackets table row cell 4 c minus 6 b end cell cell 2 a end cell row cell 4 a plus 2 end cell cell 2 b plus 14 end cell end table close square brackets end cell end table end style 

Dari kesamaan matriks ini kita peroleh nilai a, b, dan c sebagai berikut.

begin mathsize 14px style 4 equals 2 a left right double arrow a equals 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 b end cell equals cell 4 a plus 2 end cell row cell 2 b end cell equals cell 4 times 2 plus 2 end cell row cell 2 b end cell equals 10 row b equals 5 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 c end cell equals cell 2 b plus 14 end cell row cell 3 c end cell equals cell 2 times 5 plus 14 end cell row cell 3 c end cell equals 24 row c equals 8 end table end style 

Jadi, jawaban yang tepat adalah D.

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