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  4. If A = [3&x-1 2x+3&x+2] is a symmetric matrix, then the value of x is

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

WBJEEWBJEE 2011Matrices

Solution:

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