Question

If A =$\left[\begin{array}{ccc}-1& 2& 3\\ 2& 5& x\\ 3& 3& 7\end{array}\right]$ is a symmetric matrix then find x

Answer 1

Correct matrix is

$A=\left[\begin{array}{ccc}-1& 2& 3\\ 2& 5& x\\ 3& 3& 7\end{array}\right]$

Now for symmetric matrix

$A+A^T$

$\Rightarrow \left[\begin{array}{ccc}-1& 2& 3\\ 2& 5& x\\ 3& 3& 7\end{array}\right]=\left[\begin{array}{ccc}-1& 2& 3\\ 2& 5& 3\\ 3& x& 7\end{array}\right]$

By comparing both side

$\therefore x=3$