Question
If matrix $X=\left[\begin{array}{cc}-3 & 4 \\ 2 & -3\end{array}\right]\left[\begin{array}{c}2 \\ -2\end{array}\right]$ and $2 X-3 Y=\left[\begin{array}{c}10 \\ -8\end{array}\right];$ Find the matrix $X$ and $Y$
✓
Answer
$\begin{array}{l}X=\left[\begin{array}{cc}-3 & 4 \\ 2 & -3\end{array}\right]\left[\begin{array}{c}2 \\ -2\end{array}\right]\end{array} $
$ =\left[\begin{array}{c}-6-8 \\ 4+6\end{array}\right] $
$ =\left[\begin{array}{c}-14 \\ 10\end{array}\right]$
$\begin{array}{l}\text { Given } 2 X-3 Y=\left[\begin{array}{c}10 \\ -8\end{array}\right] \end{array} $
$ 2\left[\begin{array}{c}-14 \\ 10\end{array}\right]-3 Y=\left[\begin{array}{c}10 \\ -8\end{array}\right] $
$ 3 Y=2\left[\begin{array}{c}-14 \\ 10\end{array}\right]-\left[\begin{array}{c}10 \\ -8\end{array}\right] $
$ 3 Y=\left[\begin{array}{c}-38 \\ 28\end{array}\right] $
$ Y=\frac{1}{3}\left[\begin{array}{c}-38 \\ 28\end{array}\right]$
$ =\left[\begin{array}{c}-6-8 \\ 4+6\end{array}\right] $
$ =\left[\begin{array}{c}-14 \\ 10\end{array}\right]$
$\begin{array}{l}\text { Given } 2 X-3 Y=\left[\begin{array}{c}10 \\ -8\end{array}\right] \end{array} $
$ 2\left[\begin{array}{c}-14 \\ 10\end{array}\right]-3 Y=\left[\begin{array}{c}10 \\ -8\end{array}\right] $
$ 3 Y=2\left[\begin{array}{c}-14 \\ 10\end{array}\right]-\left[\begin{array}{c}10 \\ -8\end{array}\right] $
$ 3 Y=\left[\begin{array}{c}-38 \\ 28\end{array}\right] $
$ Y=\frac{1}{3}\left[\begin{array}{c}-38 \\ 28\end{array}\right]$
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