Question

Find $x+y$ if $\left[\begin{array}{cc}-2& 0\\ 3& 1\end{array}\right]\left[\begin{array}{c}-1\\ 2x\end{array}\right]+3\left[\begin{array}{c}-2\\ 1\end{array}\right]=2\left[\begin{array}{c}y\\ 3\end{array}\right].$

Answer 1

Consider, $\left[\begin{array}{cc}-2& 0\\ 3& 1\end{array}\right]\left[\begin{array}{c}-1\\ 2x\end{array}\right]+3\left[\begin{array}{c}-2\\ 1\end{array}\right]=2\left[\begin{array}{c}y\\ 3\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}2\\ -3+2x\end{array}\right]+\left[\begin{array}{c}-6\\ 3\end{array}\right]=\left[\begin{array}{c}2y\\ 6\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}-4\\ 2x\end{array}\right]=\left[\begin{array}{c}2y\\ 6\end{array}\right]$

$\Rightarrow -4=2y$ and $2x=6$

$\Rightarrow y=-2$ and $x=3$

$\therefore x+y=3-2=1$