Question
If $\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right]+2 M=3\left[\begin{array}{cc}3 & 2 \\ 0 & -3\end{array}\right]$, find the matrix $M$
✓
Answer
$\begin{aligned} & {\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right]+2 M =3\left[\begin{array}{cc}3 & 2 \\ 0 & -3\end{array}\right]} \\ & 2 M =3\left[\begin{array}{cc}3 & 2 \\ -2 & 3\end{array}\right]-\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right] \\ & =\left[\begin{array}{cc}9 & 6 \\ 0 & -9\end{array}\right]-\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right] \\ & =\left[\begin{array}{cc}9-1 & 6-4 \\ 0-(-2) & -9-3\end{array}\right] \\ & =\left[\begin{array}{cc}8 & 2 \\ 2 & -12\end{array}\right] \\ & \therefore M =\frac{1}{2}\left[\begin{array}{cc}8 & 2 \\ 2 & -12\end{array}\right] \\ & =\left[\begin{array}{cc}4 & 1 \\ 1 & -6\end{array}\right] . . . \text { (Dividing by } 2 \text { ) }\end{aligned}$
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