Question
If $A=\left[\begin{array}{cc}0 & -1 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 2 \\ -1 & 1\end{array}\right]$ Find the matrix $X$ if : $3 A+X=B$
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Answer
$\begin{aligned} & A=\left[\begin{array}{cc}0 & -1 \\ 1 & 2\end{array}\right] \\ & B=\left[\begin{array}{cc}1 & 2 \\ -1 & 1\end{array}\right] \\ & 3 A + X = B \\ & \Rightarrow X = B -3 A \\ & X=\left[\begin{array}{cc}1 & 2 \\ -1 & 1\end{array}\right]-3\left[\begin{array}{cc}0 & -1 \\ 1 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}1 & 2 \\ -1 & 1\end{array}\right]-\left[\begin{array}{cc}0 & -3 \\ 3 & 6\end{array}\right] \\ & =\left[\begin{array}{cc}1-0 & 2+3 \\ -1-3 & 1-6\end{array}\right] \\ & =\left[\begin{array}{cc}1 & 5 \\ -4 & -5\end{array}\right] \text {. } \\ & \end{aligned}$
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