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Diketahui  Jika AX = B dan BC = D, maka X = ....

Pertanyaan

Diketahui begin mathsize 14px style straight A equals open parentheses table row 1 0 row 2 cell negative 3 end cell end table close parentheses comma straight C equals open parentheses table row 0 2 row cell negative 1 end cell cell negative 4 end cell end table close parentheses comma straight D equals open parentheses table row 5 2 row cell negative 3 end cell 0 end table close parentheses. end style Jika AX = B dan BC = D, maka X = ....

  1. begin mathsize 14px style 1 third open parentheses table row 27 15 row 24 13 end table close parentheses end style 

  2. begin mathsize 14px style negative 1 third open parentheses table row 27 15 row 24 13 end table close parentheses end style 

  3. begin mathsize 14px style open parentheses table row 27 15 row 24 13 end table close parentheses end style 

  4. begin mathsize 14px style 1 third open parentheses table row 24 13 row 27 15 end table close parentheses end style 

  5. begin mathsize 14px style open parentheses table row cell negative 24 end cell cell negative 13 end cell row cell negative 27 end cell cell negative 15 end cell end table close parentheses end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui AX = B, maka jika kita kalikan matriks undefined kedua ruas di kiri menjadi

undefined 

Selanjutnya, diketahui BC = D, maka jika kita kalikan matriks undefined kedua ruas di kanan menjadi

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BCC to the power of negative 1 end exponent end cell equals cell DC to the power of negative 1 end exponent end cell row straight B equals cell DC to the power of negative 1 end exponent end cell row blank blank blank end table end style 

Ingat bahwa jika 

undefined 

Maka

undefined 

Sehingga kita punya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight X equals cell straight A to the power of negative 1 end exponent straight B end cell row blank equals cell straight A to the power of negative 1 end exponent DC to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator 1 open parentheses negative 3 close parentheses minus 0 open parentheses 2 close parentheses end fraction open parentheses table row cell negative 3 end cell 0 row cell negative 2 end cell 1 end table close parentheses open parentheses table row 5 2 row cell negative 3 end cell 0 end table close parentheses fraction numerator 1 over denominator 0 open parentheses negative 4 close parentheses minus 2 open parentheses negative 1 close parentheses end fraction open parentheses table row cell negative 4 end cell cell negative 2 end cell row 1 0 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 3 end fraction open parentheses table row cell negative 3 end cell 0 row cell negative 2 end cell 1 end table close parentheses open parentheses table row 5 2 row cell negative 3 end cell 0 end table close parentheses 1 half open parentheses table row cell negative 4 end cell cell negative 2 end cell row 1 0 end table close parentheses end cell row blank equals cell open parentheses table row 1 0 row cell 2 over 3 end cell cell negative 1 third end cell end table close parentheses open parentheses table row 5 2 row cell negative 3 end cell 0 end table close parentheses open parentheses table row cell negative 2 end cell cell negative 1 end cell row cell 1 half end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row 5 2 row cell 10 over 3 plus 1 end cell cell 4 over 3 end cell end table close parentheses open parentheses table row cell negative 2 end cell cell negative 1 end cell row cell 1 half end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row 5 2 row cell 13 over 3 end cell cell 4 over 3 end cell end table close parentheses open parentheses table row cell negative 2 end cell cell negative 1 end cell row cell 1 half end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 10 plus 1 end cell cell negative 5 end cell row cell negative 26 over 3 plus 2 over 3 end cell cell negative 13 over 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 9 end cell cell negative 5 end cell row cell negative 8 end cell cell negative 13 over 3 end cell end table close parentheses end cell row blank equals cell negative 1 third open parentheses table row 27 15 row 24 13 end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah B.

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