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If \(A=\left(\begin{array}{cc}3 & x-1 \\ 2 x+3 & x+2\end{array}\right)\) is a symmetric matrix, then the value of \(x\) is
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Verified Answer
The correct answer is:
-4
Hints: \(A=A^T\)
\(\begin{aligned}
& \left(\begin{array}{cc}
3 & x-1 \\
2 x+3 & x+2
\end{array}\right)=\left(\begin{array}{cc}
3 & 2 x+3 \\
x-1 & x+2
\end{array}\right) \\
& \Rightarrow x-1=2 x+3 \text { or } x=-4
\end{aligned}\)
\(\begin{aligned}
& \left(\begin{array}{cc}
3 & x-1 \\
2 x+3 & x+2
\end{array}\right)=\left(\begin{array}{cc}
3 & 2 x+3 \\
x-1 & x+2
\end{array}\right) \\
& \Rightarrow x-1=2 x+3 \text { or } x=-4
\end{aligned}\)
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