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SMK Teknologi dan Rekayasa

Solusi Paket 59 UN 2011 Matematika SMK Teknologi (21)


Diketahui\ matriks\ A=\begin{pmatrix} 8 & 1 \\ 2 & -3 \end{pmatrix},\ B=\begin{pmatrix} 1 & 4 \\ 5 & 0 \end{pmatrix},\ dan\ C=\begin{pmatrix} 2 & -1 \\ 3 & 4 \end{pmatrix}\\\\maka\ nilai\ \ 2A-B+3C\ \ adalah\ ....\\\\A.\ \ \begin{pmatrix} 9 & -4 \\ 0 & 1 \end{pmatrix}\ \ \ \ \ \ \ \ \ \ B.\ \ \begin{pmatrix} 21 & -5 \\ 8 & 6 \end{pmatrix}\ \ \ \ \ \ \ \ \ \ C.\ \ \begin{pmatrix} 17 & -3 \\ 2 & -2 \end{pmatrix}\\\\\\D\ \ \begin{pmatrix} 21 & -4 \\ 8 & 1 \end{pmatrix}\ \ \ \ \ \ \ \ \ \ E.\ \ \begin{pmatrix} 9 & 1 \\ -10 & -18 \end{pmatrix}
Jawaban: B
\begin{array}{rcl}2A-B+3C\ &=&2\begin{pmatrix} 8 & 1 \\ 2 & -3 \end{pmatrix}-\begin{pmatrix} 1 & 4 \\ 5 & 0 \end{pmatrix}+3\begin{pmatrix} 2 & -1 \\ 3 & 4 \end{pmatrix}\\\\&=&\begin{pmatrix} 16 & 2 \\ 4 & -6 \end{pmatrix}-\begin{pmatrix} 1 & 4 \\ 5 & 0 \end{pmatrix}+\begin{pmatrix} 6 & -3 \\ 9 & 12 \end{pmatrix}\\\\&=&\begin{pmatrix} 16-1+6 & 2-4+(-3) \\ 4-5+9 & -6-0+12 \end{pmatrix}\\\\&=&\begin{pmatrix} 21 & -5 \\ 8 & 6\end{pmatrix}\end{array}

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