Pertanyaan

Jika X ( 2 5 4 1 ) = ( 12 31 6 17 ) maka X = ...

Jika $X (2541) = (1231617)$ maka $X =$ ...

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Pada persamaan matriks bentuk berlaku: Invers matriks berlaku: Sehingga diperoleh penyelesaiannya yaitu: Maka . Oleh karena itu, jawaban yang benar adalah B.

Pada persamaan matriks bentuk X A equals B berlaku:

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 X open parentheses table row 2 4 row 5 1 end table close parentheses end cell equals cell open parentheses table row 12 6 row 31 17 end table close parentheses end cell row X equals cell open parentheses table row 12 6 row 31 17 end table close parentheses open parentheses table row 2 4 row 5 1 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row 12 6 row 31 17 end table close parentheses times fraction numerator 1 over denominator 2 open parentheses 1 close parentheses minus 4 open parentheses 5 close parentheses end fraction open parentheses table row 1 cell negative 4 end cell row cell negative 5 end cell 2 end table close parentheses end cell row blank equals cell open parentheses table row 12 6 row 31 17 end table close parentheses times fraction numerator 1 over denominator 2 minus 20 end fraction open parentheses table row 1 cell negative 4 end cell row cell negative 5 end cell 2 end table close parentheses end cell row blank equals cell open parentheses table row 12 6 row 31 17 end table close parentheses times fraction numerator 1 over denominator negative 18 end fraction open parentheses table row 1 cell negative 4 end cell row cell negative 5 end cell 2 end table close parentheses end cell row blank equals cell open parentheses table row 12 6 row 31 17 end table close parentheses open parentheses table row cell negative 1 over 18 end cell cell fraction numerator negative 4 over denominator negative 18 end fraction end cell row cell fraction numerator negative 5 over denominator negative 18 end fraction end cell cell fraction numerator 2 over denominator negative 18 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row 12 6 row 31 17 end table close parentheses open parentheses table row cell negative 1 over 18 end cell cell 2 over 9 end cell row cell 5 over 18 end cell cell negative 1 over 9 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 12 open parentheses negative 1 over 18 close parentheses plus 6 open parentheses 5 over 18 close parentheses end cell cell 12 open parentheses 2 over 9 close parentheses plus 6 open parentheses negative 1 over 9 close parentheses end cell row cell 31 open parentheses negative 1 over 18 close parentheses plus 17 open parentheses 5 over 18 close parentheses end cell cell 31 open parentheses 2 over 9 close parentheses plus 17 open parentheses negative 1 over 9 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 12 over 18 plus 30 over 18 end cell cell 24 over 9 minus 6 over 9 end cell row cell negative 31 over 18 plus 85 over 18 end cell cell 62 over 9 minus 17 over 9 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 18 over 18 end cell cell 18 over 9 end cell row cell 54 over 18 end cell cell 45 over 9 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 2 row 3 5 end table close parentheses end cell end table$

Maka X equals open parentheses table row 1 2 row 3 5 end table close parentheses .

Oleh karena itu, jawaban yang benar adalah B.