If the matrix $\begin{bmatrix}-3 & x-y & 5\\1& 0 & z\\x+y & 4 & 7\end{bmatrix}$ is symmetric, then the correct option of the following, is :

$x=3, y=2, z=4 $

Given matrix:

$\begin{pmatrix} -3 & x-y & 5 \\ 1 & 0 & z \\ x+y & 4 & 7 \end{pmatrix}$

For a symmetric matrix, $a_{ij}=a_{ji}$.

So:

$x-y=1$ …(1)

$5=x+y$ …(2)

$z=4$ …(3)

Add (1) and (2):

$2x=6 \Rightarrow x=3$

Substitute in (2):

$3+y=5 \Rightarrow y=2$

From (3):

$z=4$

final answer: $x=3,\;y=2,\;z=4$