Question

If $\left[\begin{array}{cc}x+y& 2x+z\\ x-y& 2z+w\end{array}\right]=\left[\begin{array}{cc}4& 7\\ 0& 10\end{array}\right]$, then find $y+z+w$

Answer 1

We have $\left[\begin{array}{cc}x+y& 2x+z\\ x-y& 2z+w\end{array}\right]=\left[\begin{array}{cc}4& 7\\ 0& 10\end{array}\right]$
Comparing the elements we have
$x+y=4,2x+z=7,x-y=0$ and $2z+w=10$
Solving these equations we get $x=2$ and $y=2,z=3,w=4$
then $y+z+w=9$