Question

If $A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is a symmetric matrix, then x = ______________.

Answer 1

The given matrix $A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is symmetric.

$\therefore A^T=A$

$\Rightarrow {\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]}^T=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}4& 2x-3\\ x+2& x+1\end{array}\right]=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$

$\Rightarrow 2x-3=x+2$

$\Rightarrow x=5$

If $A=\left[\begin{array}{cc}4& x+2\\ 2x-3& x+1\end{array}\right]$ is a symmetric matrix, then x = ____5____.