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

Pertanyaan

Diketahui begin mathsize 14px style straight P equals open parentheses table row straight a 1 4 row straight a 0 cell negative 1 end cell end table close parentheses space dan space straight Q equals open parentheses table row 0 4 row straight x 2 row 0 cell negative 1 end cell end table close parentheses end style . Jika det(PQ) = -7x dan ≠ 0, maka = ....

  1. 2

  2. 1

  3. 0

  4. undefined2

  5. undefined4

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

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 left parenthesis PQ right parenthesis equals detP times detQ 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 1 4 row straight a 0 cell negative 1 end cell end table close parentheses space open parentheses table row 0 4 row straight x 2 row 0 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell straight a times 0 plus 1 times straight x plus 4 times 0 end cell cell straight a times 4 plus 1 times 2 plus 4 times left parenthesis negative 1 right parenthesis end cell row cell straight a times 0 plus 0 times straight x plus left parenthesis negative 1 right parenthesis times 0 end cell cell straight a times 4 plus 0 times 2 plus left parenthesis negative 1 right parenthesis times left parenthesis negative 1 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 0 plus straight x plus 0 end cell cell 4 straight a plus 2 minus 4 end cell row cell 0 plus 0 plus 0 end cell cell 4 straight a plus 0 plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row straight x cell 4 straight a minus 2 end cell row 0 cell 4 straight a plus 1 end cell end table close parentheses end cell end table end style  

 

Sehingga

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 left parenthesis straight x right parenthesis times left parenthesis 4 straight a plus 1 right parenthesis minus left parenthesis 4 straight a minus 2 right parenthesis times left parenthesis 0 right parenthesis end cell row blank equals cell 4 ax plus straight x minus 0 end cell row blank equals cell straight x left parenthesis 4 straight a plus 1 right parenthesis end cell end table 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 straight x left parenthesis 4 straight a plus 1 right parenthesis end cell row cell negative 7 straight x end cell equals cell straight x left parenthesis 4 straight a plus 1 right parenthesis semicolon straight x not equal to 0 end cell row cell negative fraction numerator 7 straight x over denominator straight x end fraction end cell equals cell 4 straight a plus 1 end cell row cell negative 7 end cell equals cell 4 straight a plus 1 end cell row cell negative 4 straight a end cell equals cell 1 plus 7 end cell row cell negative 4 straight a end cell equals 8 row straight a equals cell fraction numerator 8 over denominator negative 4 end fraction end cell row straight a equals cell negative 2 end cell end table end style 

Jadi, jawaban yang tepat adalah D.

42

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