Question

If $\left[\begin{array}{cc}x-y& z\\ 2x-y& w\end{array}\right]=\left[\begin{array}{cc}-1& 4\\ 0& 5\end{array}\right]$, find the value of $x+y.$

Answer 1

Since $\left(\begin{array}{cc}x-y& z\\ 2x-y& w\end{array}\right)=\left(\begin{array}{cc}-1& 4\\ 0& 5\end{array}\right)$

Equating the matrices we get,

$x-y=-1................\left(1\right)$

$z=4................\left(2\right)$

$2x-y=0................\left(3\right)$

$w=5................\left(4\right)$

Now from equation (3) we get $y=2x$

Substituting $y=2x$ in equation (1) we get,

$x-2x=-1⟹-x=-1⟹x=1$

Therefore, $x=1$.

Now put $x=1$ in $y=2x$, then $y=2$.

And $x+y=1+2=3$

Hence, $x+y=3$.