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SMK Teknologi dan Rekayasa

Soal 42 Operasi Matriks


Jika\ matriks\ A=\begin{pmatrix} 0 & -1 & 1\\ 1 & 2 & 1\\ -2 & 2 & 4 \end{pmatrix},\ maka\ determinan\ matriks\ A\\adalah\ \left | A \right |=\ ....\\a.\ \ 6\ \ \ \ \ \ \ \ \ \ b.\ -6\ \ \ \ \ \ \ \ \ \ c.\ \ 8\ \ \ \ \ \ \ \ \ \ d.\ \ 10\ \ \ \ \ \ \ \ \ \ e.\ \ 12
Jawaban: e
\begin{array}{rcl}\left | A \right |&=&\left.\begin{pmatrix} 0 & -1 & 1\\ 1 & 2 & 1\\ -2 & 2 & 4 \end{pmatrix}\right|\begin{matrix} 0 & -1\\ 1 & 2\\ -2 & 2 \end{matrix}\\\\&=&0.2.4+(-1).1.(-2)+1.1.2-1.2.(-2)-0.1.2-(-1).1.4\\\\&=&0+2+2-(-4)-0-(-4)\\\\&=&12\end{array}

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