If \begin{bmatrix} x-y & z \ 2x-y & w \end{bmatrix} = \begin{bmatrix} 0 & 4 \ 0 & 5 \end{bmatrix}, find the value of x+y.

Since \begin{bmatrix} x-y & z \ 2x-y & w \end{bmatrix} = \begin{bmatrix} 0 & 4 \ 0 & 5 \end{bmatrix}
Equating the matrices we get,
x-y=0 (1)
z=4 (2)
2x-y=0 (3)
w=5 (4)
Now from equation (3) we get
y=2x
Substituting y=2x in equation (1) we get,
x-2x=0
-x=0
x=0
Therefore, x=0.
Now put x=0 in y=2x, then y=0.
And x+y=0+0=0
Hence, x+y=0.