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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
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.
$-4$
$\because A$ is a symmetric matrix
$\Rightarrow A^T=A$
$\Rightarrow\left[\begin{array}{cc}
3 & 2 x+3 \\
x-1 & x+2
\end{array}\right]=\left[\begin{array}{cc}
3 & x-1 \\
2 x+3 & x+2
\end{array}\right]$
$\Rightarrow x-1=2 x+3$
$\Rightarrow x=-4$

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