Jika matriks M memenuhi persamaan M⋅[312−1]=[2113] Maka determinan matriks M adalah ....

Pertanyaan

Jika matriks M memenuhi persamaan

$M\cdot\begin{bmatrix}3&2\\1&-1\end{bmatrix}=\begin{bmatrix}2&1\\1&3\end{bmatrix}$

Maka determinan matriks M adalah ....

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benara adalah E.

Pembahasan

Diketahui, M times open square brackets table row 3 2 row 1 cell negative 1 end cell end table close square brackets equals open square brackets table row 2 1 row 1 3 end table close square brackets , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell M times open square brackets table row 3 2 row 1 cell negative 1 end cell end table close square brackets end cell equals cell open square brackets table row 2 1 row 1 3 end table close square brackets end cell row M equals cell open square brackets table row 2 1 row 1 3 end table close square brackets times fraction numerator 1 over denominator negative 3 minus 2 end fraction open square brackets table row cell negative 1 end cell cell negative 2 end cell row cell negative 1 end cell 3 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator negative 5 end fraction open square brackets table row 2 1 row 1 3 end table close square brackets open square brackets table row cell negative 1 end cell cell negative 2 end cell row cell negative 1 end cell 3 end table close square brackets end cell row blank equals cell negative 1 fifth open square brackets table row cell negative 3 end cell cell negative 1 end cell row cell negative 4 end cell 7 end table close square brackets end cell row cell open vertical bar M close vertical bar end cell equals cell negative 1 fifth open parentheses negative 21 minus 4 close parentheses end cell row blank equals cell negative 1 fifth cross times open parentheses negative 25 close parentheses end cell row blank equals 5 end table$

Oleh karena itu, jawaban yang benara adalah E.