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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 cell negative 1 end cell row cell negative 3 end cell 5 end table close parentheses comma space straight C equals open parentheses table row 0 4 row cell negative 6 end cell cell negative 2 end cell end table close parentheses comma space straight D equals open parentheses table row cell negative 6 end cell 9 row 2 cell negative 5 end cell end table close parentheses. end style Jika begin mathsize 14px style AX equals straight B end style dan begin mathsize 14px style BC equals straight D end style, maka begin mathsize 14px style straight X equals end style ....

  1. begin mathsize 14px style 1 over 6 open parentheses table row cell negative 74 end cell 28 row 41 cell negative 16 end cell end table close parentheses end style  

  2. begin mathsize 14px style 1 over 12 open parentheses table row cell negative 74 end cell 28 row 41 cell negative 16 end cell end table close parentheses end style 

  3. begin mathsize 14px style open parentheses table row 74 28 row 41 16 end table close parentheses end style 

  4. begin mathsize 14px style 1 over 6 open parentheses table row 74 28 row 41 16 end table close parentheses end style 

  5. begin mathsize 14px style 1 over 12 open parentheses table row 74 28 row 41 16 end table close parentheses end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Diketahui begin mathsize 14px style AX equals straight B end style, maka jika kita kalikan matriks undefined  kedua ruas di kiri menjadi

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

Selanjutnya, diketahui begin mathsize 14px style BC equals straight D end style, maka jika kita kalikan matriks begin mathsize 14px style straight C to the power of negative 1 end exponent end style 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 end table end style 

Ingat bahwa jika

begin mathsize 14px style straight M equals open parentheses table row straight a straight b row straight c straight d end table close parentheses end style 

Maka

begin mathsize 14px style straight M to the power of negative 1 end exponent equals fraction numerator 1 over denominator ad minus bc end fraction open parentheses table row straight d cell negative straight b end cell row cell negative straight c end cell straight a end table close parentheses end style 

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 left parenthesis 5 right parenthesis minus left parenthesis negative 1 right parenthesis left parenthesis negative 3 right parenthesis end fraction open parentheses table row 5 1 row 3 1 end table close parentheses open parentheses table row cell negative 6 end cell 9 row 2 cell negative 5 end cell end table close parentheses fraction numerator 1 over denominator 0 left parenthesis negative 2 right parenthesis minus 4 left parenthesis negative 6 right parenthesis end fraction open parentheses table row cell negative 2 end cell cell negative 4 end cell row 6 0 end table close parentheses end cell row blank equals cell 1 half open parentheses table row 5 1 row 3 1 end table close parentheses open parentheses table row cell negative 6 end cell 9 row 2 cell negative 5 end cell end table close parentheses 1 over 24 open parentheses table row cell negative 2 end cell cell negative 4 end cell row 6 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 5 over 2 end cell cell 1 half end cell row cell 3 over 2 end cell cell 1 half end cell end table close parentheses open parentheses table row cell negative 6 end cell 9 row 2 cell negative 5 end cell end table close parentheses open parentheses table row cell negative 1 over 12 end cell cell negative 1 over 6 end cell row cell 1 fourth end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 15 plus 1 end cell cell 45 over 2 minus 5 over 2 end cell row cell negative 9 plus 1 end cell cell 27 over 2 minus 5 over 2 end cell end table close parentheses open parentheses table row cell negative 1 over 12 end cell cell negative 1 over 6 end cell row cell 1 fourth end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 14 end cell 20 row cell negative 8 end cell 11 end table close parentheses open parentheses table row cell negative 1 over 12 end cell cell negative 1 over 6 end cell row cell 1 fourth end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 7 over 6 plus 5 end cell cell 7 over 3 end cell row cell 2 over 3 plus 11 over 4 end cell cell 4 over 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 37 over 6 end cell cell 7 over 3 end cell row cell 41 over 12 end cell cell 4 over 3 end cell end table close parentheses end cell row blank equals cell 1 over 12 open parentheses table row 74 28 row 41 16 end table close parentheses end cell end table end style

Jadi, jawaban yang tepat adalah E.

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