If $\begin{bmatrix}x+y&4\\1+z&y\end{bmatrix}=\begin{bmatrix}2&4\\5&6\end{bmatrix}$, then

$x=-4, y=6,z= 4$

The correct answer is Option (2) → $x=-4, y=6,z= 4$

Given:

$\begin{pmatrix}x+y & 4 \\ 1+z & y\end{pmatrix} =\begin{pmatrix}2 & 4 \\ 5 & 6\end{pmatrix}$

Equate corresponding entries:

$x+y=2$

$4=4$ (always true)

$1+z=5\Rightarrow z=4$

$y=6$

Now substitute $y=6$ into $x+y=2$:

$x+6=2\Rightarrow x=-4$

Thus $x=-4,\;y=6,\;z=4$.