Question
If $A=\left[\begin{array}{cc}3 & x-1 \\ 2 x+3 & x+2\end{array}\right]$ is a symmetric matrix, then $x=$
✓
Answer
$(c) \because A$ is a symmetric matrix $\Rightarrow A^T=A$
$\Rightarrow\left[\begin{array}{cc} 3 & 2 x+3 \\ x-1 & x+2 \end{array}\right]$
$=\left[\begin{array}{cc} 3 & x-1 \\ 2 x+3 & x+2 \end{array}\right] $
$\Rightarrow x-1=2 x+3$
$\Rightarrow x=-4 $
$\Rightarrow\left[\begin{array}{cc} 3 & 2 x+3 \\ x-1 & x+2 \end{array}\right]$
$=\left[\begin{array}{cc} 3 & x-1 \\ 2 x+3 & x+2 \end{array}\right] $
$\Rightarrow x-1=2 x+3$
$\Rightarrow x=-4 $
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