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 $M$
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Answer
$\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right]+2 M=3\left[\begin{array}{cc}3 & 2 \\ 0 & -3\end{array}\right]$
$\begin{array}{l}\Rightarrow 2 M=\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}8 & 2 \\ 2 & -12\end{array}\right] \end{array} $
$ \Rightarrow M=\left[\begin{array}{cc}4 & 1 \\ 1 & -6\end{array}\right]$
$\begin{array}{l}\Rightarrow 2 M=\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}8 & 2 \\ 2 & -12\end{array}\right] \end{array} $
$ \Rightarrow M=\left[\begin{array}{cc}4 & 1 \\ 1 & -6\end{array}\right]$
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