Question

Find $x,$ if the matrix $\left|\begin{array}{ccc}-1& 2& 3\\ 2& 5& 6\\ 3& x& 7\end{array}\right|$ is a symmetric matrix.

Answer 1

Let $A=\left[\begin{array}{c}-123\\ 256\\ 3x7\end{array}\right]$

$A^{\prime }=\left[\begin{array}{c}-123\\ 25x\\ 367\end{array}\right]$

If $A$ is symmetric ,

Then $A=A^{\prime }$

Therefore,

$x=6$