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Pertanyaan

Jika open parentheses table row 2 3 row 1 2 end table close parentheses open parentheses table row x row y end table close parentheses equals open parentheses table row 4 row 5 end table close parentheses maka nilai x squared minus y squared equals ...

  1. negative 13

  2. negative 1

  3. 0

  4. 1

  5. 13

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Lakukan penyelesaian SPL pada matriks dengan metode invers.

Invers matriks 2 cross times 2 berlaku:

open parentheses table row a b row c d end table close parentheses to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses

Sehingga diperoleh penyelesaiannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 2 3 row 1 2 end table close parentheses open parentheses table row x row y end table close parentheses end cell equals cell open parentheses table row 4 row 5 end table close parentheses end cell row cell open parentheses table row x row y end table close parentheses end cell equals cell open parentheses table row 2 3 row 1 2 end table close parentheses to the power of negative 1 end exponent times open parentheses table row 4 row 5 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 2 open parentheses 2 close parentheses minus 3 open parentheses 1 close parentheses end fraction open parentheses table row 2 cell negative 3 end cell row cell negative 1 end cell 2 end table close parentheses open parentheses table row 4 row 5 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 minus 3 end fraction open parentheses table row 2 cell negative 3 end cell row cell negative 1 end cell 2 end table close parentheses open parentheses table row 4 row 5 end table close parentheses end cell row blank equals cell 1 over 1 open parentheses table row 2 cell negative 3 end cell row cell negative 1 end cell 2 end table close parentheses open parentheses table row 4 row 5 end table close parentheses end cell row blank equals cell 1 times open parentheses table row 2 cell negative 3 end cell row cell negative 1 end cell 2 end table close parentheses open parentheses table row 4 row 5 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 open parentheses 4 close parentheses plus open parentheses negative 3 close parentheses open parentheses 5 close parentheses end cell row cell negative 1 open parentheses 4 close parentheses plus 2 open parentheses 5 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 8 minus 15 end cell row cell negative 4 plus 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 7 end cell row 6 end table close parentheses end cell end table

Maka x equals negative 7 dan y equals 6.

Sehingga diperoleh nilainya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus y squared end cell equals cell open parentheses negative 7 close parentheses squared minus 6 squared end cell row blank equals cell 49 minus 36 end cell row blank equals 13 end table

Oleh karena itu, jawaban yang benar adalah E.

35

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