Question

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

• A. $4$
• B. $3$
• C. $-4$
• D. $-3$

Answer 1

The correct option is C

$-4$

Explanation for the correct option:

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

$\Rightarrow$ $A^T=A$

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

$\because$Both the matrices are equal, Compare the corresponding elements:

$\Rightarrow$$2x+3=x-1$

$\mathbf{\therefore }\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{4}$

Hence, Option ‘C’ is Correct.