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Pertanyaan

Diketahui matriks-matriks begin mathsize 14px style straight A equals open parentheses table row cell 2 x minus 3 z end cell 5 row cell z minus 3 end cell 9 end table close parentheses end stylebegin mathsize 14px style straight B equals open parentheses table row 2 cell negative 1 end cell row 1 cell z minus 4 end cell end table close parentheses end stylebegin mathsize 14px style straight C equals open parentheses table row 2 1 row cell negative 9 end cell y end table close parentheses end style. Jika begin mathsize 14px style straight B to the power of straight T end style adalah transpose dari matriks begin mathsize 14px style straight B end style dan begin mathsize 14px style straight A plus straight B to the power of straight T minus straight C equals open parentheses table row 3 5 row 4 6 end table close parentheses end style, maka nilai begin mathsize 14px style x plus y plus z end style adalah begin mathsize 14px style.... end style

  1. begin mathsize 14px style 1 end style

  2. begin mathsize 14px style 0 end style

  3. begin mathsize 14px style negative 1 end style

  4. begin mathsize 14px style negative 2 end style

  5. begin mathsize 14px style negative 3 end style

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Pembahasan

Kita cari transpose dari matriks begin mathsize 14px style straight B end style terlebih dahulu.

begin mathsize 14px style straight B equals open parentheses table row 2 cell negative 1 end cell row 1 cell z minus 4 end cell end table close parentheses straight B to the power of straight T equals open parentheses table row 2 1 row cell negative 1 end cell cell z minus 4 end cell end table close parentheses end style

Kemudian kita kerjakan penjumlahan dan pengurangan matriks yang diminta pada soal.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight A plus straight B to the power of straight T minus straight C end cell equals cell open parentheses table row 3 5 row 4 6 end table close parentheses end cell row cell open parentheses table row cell 2 x minus 3 z end cell 5 row cell z minus 3 end cell 9 end table close parentheses plus open parentheses table row 2 1 row cell negative 1 end cell cell z minus 4 end cell end table close parentheses minus open parentheses table row 2 1 row cell negative 9 end cell y end table close parentheses end cell equals cell open parentheses table row 3 5 row 4 6 end table close parentheses end cell row cell open parentheses table row cell 2 x minus 3 z end cell 5 row cell z plus 5 end cell cell z minus y plus 5 end cell end table close parentheses end cell equals cell open parentheses table row 3 5 row 4 6 end table close parentheses end cell end table end style

Kita cari nilai begin mathsize 14px style x comma space y comma space z end style dari kesamaan matriks di atas.

- Nilai begin mathsize 14px style z end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell z plus 5 end cell equals 4 row z equals cell 4 minus 5 end cell row blank equals cell negative 1 end cell end table end style

- Nilai begin mathsize 14px style x end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 3 z end cell equals 3 row cell 2 x minus 3 open parentheses negative 1 close parentheses end cell equals 3 row cell 2 x plus 3 end cell equals 3 row cell 2 x end cell equals 0 row x equals 0 end table end style

- Nilai begin mathsize 14px style y end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell z minus y plus 5 end cell equals 6 row cell negative 1 minus y plus 5 end cell equals 6 row cell negative y end cell equals cell 6 minus 4 end cell row y equals cell negative 2 end cell end table end style

Nilai begin mathsize 14px style x plus y plus z equals 0 plus open parentheses negative 2 close parentheses plus open parentheses negative 1 close parentheses equals negative 3 end style.

Jadi, jawaban yang tepat adalah E.

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