If A= [ cc 3 & x-1 2 x+3 & x+2 ] is a symmetric matrix, then x=

MCQ

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

A
4
B
3
✓
-4
D
-3

✓

Answer

Correct option: C.

-4

(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]
$
$
\begin{array}{l}
\Rightarrow \quad x-1=2 x+3 \\
\Rightarrow \quad x=-4
\end{array}
$

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