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

Solution:
Given that:

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

From above,

$x-y=-1,z=4$

$2x-y=0,w=5$

$x-y=-1$ ..........(i)

$2x-y=0$ .........(ii)

Solving eqn. (i) and (ii) we get,

$x=1$ and $y=2$

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