Pertanyaan

Jika P [ 6 8 7 9 ] = [ 2 4 3 5 ] , maka P = …

Jika $P [6879] = [2435]$ , maka $P = \dots$

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M. Mariyam

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Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Ingat kembali konsep invers pada matriks sebagai berikut: Misalkan matriks serta mempunyai sifat invers matriks Oleh karena itu, jika , maka Dengan demikian, matriks . Jadi, pilihan jawaban yang tepat adalah C.

Ingat kembali konsep invers pada matriks sebagai berikut:

Misalkan matriks $straight A equals open parentheses table row a b row c d end table close parentheses rightwards double arrow straight A to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses$

serta mempunyai sifat invers matriks XA equals straight B rightwards double arrow X equals straight B times straight A to the power of negative 1 end exponent

Oleh karena itu, jika straight P open square brackets table row 6 7 row 8 9 end table close square brackets equals open square brackets table row 2 3 row 4 5 end table close square brackets , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight P open square brackets table row 6 7 row 8 9 end table close square brackets end cell equals cell open square brackets table row 2 3 row 4 5 end table close square brackets end cell row straight P equals cell open square brackets table row 2 3 row 4 5 end table close square brackets times open square brackets table row 6 7 row 8 9 end table close square brackets to the power of negative 1 end exponent end cell row blank equals cell open square brackets table row 2 3 row 4 5 end table close square brackets times fraction numerator 1 over denominator 6 open parentheses 9 close parentheses minus 7 open parentheses 8 close parentheses end fraction open square brackets table row 9 cell negative 7 end cell row cell negative 8 end cell 6 end table close square brackets end cell row blank equals cell open square brackets table row 2 3 row 4 5 end table close square brackets times fraction numerator 1 over denominator 54 minus 56 end fraction open square brackets table row 9 cell negative 7 end cell row cell negative 8 end cell 6 end table close square brackets end cell row blank equals cell negative 1 half open square brackets table row 2 3 row 4 5 end table close square brackets times open square brackets table row 9 cell negative 7 end cell row cell negative 8 end cell 6 end table close square brackets end cell row blank equals cell negative 1 half open square brackets table row cell 2 open parentheses 9 close parentheses plus 3 open parentheses negative 8 close parentheses end cell cell 2 open parentheses negative 7 close parentheses plus 3 open parentheses 6 close parentheses end cell row cell 4 open parentheses 9 close parentheses plus 5 open parentheses negative 8 close parentheses end cell cell 4 open parentheses negative 7 close parentheses plus 5 open parentheses 6 close parentheses end cell end table close square brackets end cell row blank equals cell negative 1 half open square brackets table row cell 18 minus 24 end cell cell negative 14 plus 18 end cell row cell 36 minus 40 end cell cell negative 28 plus 30 end cell end table close square brackets end cell row blank equals cell negative 1 half open square brackets table row cell negative 6 end cell 4 row cell negative 4 end cell 2 end table close square brackets end cell row blank equals cell open square brackets table row 3 cell negative 2 end cell row 2 cell negative 1 end cell end table close square brackets end cell end table$

Dengan demikian, matriks straight P equals open square brackets table row 3 cell negative 2 end cell row 2 cell negative 1 end cell end table close square brackets .

Jadi, pilihan jawaban yang tepat adalah C.