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SMK Teknologi dan Rekayasa

Soal 41 Operasi Matriks


Diketahui\ matriks\ A=\begin{pmatrix} 4 & -3 \\ 5 & 2 \end{pmatrix},\ B=\begin{pmatrix} 10 & -2 \\ 4 & 6 \end{pmatrix},\ C=\begin{pmatrix} 7 & -5 \\ 1 & 3 \end{pmatrix},\\\\maka\ nilai\ \ 2A-\frac{1}{2}B+C\ \ adalah\ ....\\\\a.\ \ \begin{pmatrix} 10 & -10 \\ 9 & 3 \end{pmatrix}\ \ \ \ \ \ \ \ \ \ b.\ \ \begin{pmatrix} 20 & -12 \\ 1 & 4 \end{pmatrix}\ \ \ \ \ \ \ \ \ \ c.\ \ \begin{pmatrix} 10 & -10 \\ 9 & 4 \end{pmatrix}\\\\\\d.\ \ \begin{pmatrix} 10 & -10 \\ 13 & 4 \end{pmatrix}\ \ \ \ \ \ \ \ \ \ e.\ \ \begin{pmatrix} 10 & -12 \\ 13 & -2 \end{pmatrix}
Jawaban: c

\begin{array}{rcl}2A-\frac{1}{2}B+C\ &=&2\begin{pmatrix} 4 & -3 \\ 5 & 2 \end{pmatrix}-\frac{1}{2}\begin{pmatrix} 10 & -2 \\ 4 & 6 \end{pmatrix}+\begin{pmatrix} 7 & -5 \\ 1 & 3 \end{pmatrix}\\\\&=&\begin{pmatrix} 8 & -6 \\ 10 & 4 \end{pmatrix}-\begin{pmatrix} 5 & -1 \\ 2 & 3 \end{pmatrix}+\begin{pmatrix} 7 & -5 \\ 1 & 3 \end{pmatrix}\\\\&=&\begin{pmatrix} 8-5+7 & -6-(-1)+(-5) \\ 10-2+1 & 4-3+3 \end{pmatrix}\\\\&=&\begin{pmatrix} 10 & -10 \\ 9 & 4 \end{pmatrix}\end{array}

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