Question
Solve for $x$ and $y \left[\begin{array}{cc}-2 & 0 \\ 3 & 1\end{array}\right]\left[\begin{array}{c}-1 \\ 2 x\end{array}\right]+3\left[\begin{array}{c}-2 \\ 1\end{array}\right]=2\left[\begin{array}{l}y \\ 3\end{array}\right]$
✓
Answer
$\begin{array}{l}{\left[\begin{array}{cc}-2 & 0 \\ 3 & 1\end{array}\right]\left[\begin{array}{c}-1 \\ 2 x\end{array}\right]+3\left[\begin{array}{c}-2 \\ 1\end{array}\right]=2\left[\begin{array}{l}y \\ 3\end{array}\right]} \end{array} $
$ \Rightarrow\left[\begin{array}{c}2+0 \\ -3+2 x\end{array}\right]+\left[\begin{array}{c}-6 \\ 3\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}2 \\ -3+2 x\end{array}\right]+\left[\begin{array}{c}-6 \\ 3\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}2-6 \\ -3+2 x+3\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}-4 \\ 2 x\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right]$
$\Rightarrow 2 y=-4$ and $2 x=6$
$\Rightarrow y=-2$ and $x=3$
Thus, the values of $x$ andty are: $3,-2$
$ \Rightarrow\left[\begin{array}{c}2+0 \\ -3+2 x\end{array}\right]+\left[\begin{array}{c}-6 \\ 3\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}2 \\ -3+2 x\end{array}\right]+\left[\begin{array}{c}-6 \\ 3\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}2-6 \\ -3+2 x+3\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right] $
$ \Rightarrow\left[\begin{array}{c}-4 \\ 2 x\end{array}\right]=\left[\begin{array}{c}2 y \\ 6\end{array}\right]$
$\Rightarrow 2 y=-4$ and $2 x=6$
$\Rightarrow y=-2$ and $x=3$
Thus, the values of $x$ andty are: $3,-2$
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