$A=\begin{bmatrix} 4 & x+2\\ 2x-3 & x+1 \\ \end{bmatrix}$ is a symmetric matrix, then find x.
Answer & explanation
Correct answer: option 2
For a symmetric matrix $A$ we have $A=A^{t}$. The diagonal entries remain same after transpose and in this case the off diagonal entries are equal so we get
$A=A^{t}⇒x+2=2x-3$
so $x=5$.