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 :
Answer & explanation
Correct answer: option 3
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: $x=3,\;y=2,\;z=4$