Question

If $A = \begin{bmatrix}3&x-1;\\\ 2x+3&x;+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

• A. 4
• B. 3
• C. -4
• D. -3

Answer 1

Answer: (C)

-4

Answer 2

Since, $A$ is symmetric matrix, then $A=A'$
$\Rightarrow \begin{vmatrix}3 & x-1 \\\ 2 x+3 & x+2\end{vmatrix}=\begin{vmatrix}3 & 2 x+3 \\\ x-1 & x+2\end{vmatrix}$
$\Rightarrow x-1=2 x+3 \Rightarrow x=-4$