Question

Find the value of $x$ if,

$\left[\begin{array}{cc}3x+y& -y\\ 2y-x& 3\end{array}\right]=\left[\begin{array}{cc}1& 2\\ -5& 3\end{array}\right].$

Answer 1

$\because \left[\begin{array}{cc}3x+y& -y\\ 2y-x& 3\end{array}\right]=\left[\begin{array}{cc}1& 2\\ -5& 3\end{array}\right].$

From equality of two matrix,

$-y=2$

$\Rightarrow y=-2$

And $3x+y=1$

$\Rightarrow 3x+(-2)=1$

$\Rightarrow 3x=3$

$\Rightarrow x=1$