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Diketahui P=(aa​−22​13​) dan Q=⎝⎛​2x3​130​⎠⎞​ . Jika det (PQ) =2a, maka x - 4 = ....

Pertanyaan

Diketahui begin mathsize 14px style straight P equals open parentheses table row straight a cell negative 2 end cell 1 row straight a 2 3 end table close parentheses space dan space straight Q equals open parentheses table row 2 1 row straight x 3 row 3 0 end table close parentheses end style . Jika det (PQ) =2a, maka 4 = ....

  1. begin mathsize 14px style 18 a end style 

  2. begin mathsize 14px style 18 over straight a end style 

  3. Error converting from MathML to accessible text. 

  4. Error converting from MathML to accessible text.

  5. begin mathsize 14px style negative 18 a end style 

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa matriks P dan Q bukan matriks persegi, artinya tidak memiliki determinan. Sehingga kita tidak dapat menggunakan sifat

begin mathsize 14px style det space open parentheses PQ close parentheses space equals space det space P middle dot det space Q end style 

 

Maka dari itu, kita selesaikan dengan cara berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row PQ equals cell open parentheses table row straight a cell negative 2 end cell 1 row straight a 2 3 end table close parentheses space open parentheses table row 2 1 row straight x 3 row 3 0 end table close parentheses end cell row blank equals cell open parentheses table row cell straight a times 2 plus left parenthesis negative 2 right parenthesis times straight x plus 1 times 3 end cell cell straight a times 1 plus left parenthesis negative 2 right parenthesis times 3 plus 1 times 0 end cell row cell straight a times 2 plus 2 times straight x plus 3 times 3 end cell cell straight a times 1 plus 2 times 3 plus 3 times 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 straight a minus 2 straight x plus 3 end cell cell straight a minus 6 plus 0 end cell row cell 2 straight a plus 2 straight x plus 9 end cell cell straight a plus 6 plus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 straight a minus 2 straight x plus 3 end cell cell straight a minus 6 end cell row cell 2 straight a plus 2 straight x plus 9 end cell cell straight a plus 6 end cell end table close parentheses end cell end table end style  

 

Sehingga

 

begin mathsize 14px style equals 2 straight a squared plus 12 straight a minus 2 ax minus 12 straight x plus 3 straight a plus 18 minus 2 straight a squared minus 2 ax minus 9 straight a plus 12 straight a plus 12 straight x plus 54 equals 18 straight a minus 4 ax plus 72 end style 

 

Maka,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell det left parenthesis PQ right parenthesis end cell equals cell 18 straight a minus 4 ax plus 72 end cell row cell 2 straight a end cell equals cell 18 straight a minus 4 ax plus 72 end cell row cell 2 straight a minus 18 straight a plus 4 ax end cell equals 72 row cell negative 16 straight a plus 4 ax end cell equals 72 row cell 4 straight a left parenthesis negative 4 plus straight x right parenthesis end cell equals 72 row cell straight x minus 4 end cell equals cell fraction numerator 72 over denominator 4 straight a end fraction space end cell row cell straight x minus 4 end cell equals cell 18 over straight a end cell end table end style 

Jadi, jawaban yang tepat adalah B.

39

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Diketahui P=(aa​10​4−1​) dan Q=⎝⎛​0x0​42−1​⎠⎞​ . Jika det(PQ) = -7x dan x ≠ 0, maka a = ....

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