(C) matrix $A$ is symmetric if $A = A^T$,which implies $A_{ij} = A_{ji}$ for all $i, j$.For the given matrix $A = \begin{bmatrix} 5 & 2x+3 \\ x-2 & x+

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(C) matrix $A$ is symmetric if $A = A^T$,which implies $A_{ij} = A_{ji}$ for all $i, j$.For the given matrix $A = \begin{bmatrix} 5 & 2x+3 \\ x-2 & x+1 \end{bmatrix}$,the condition for symmetry is $A_{12} = A_{21}$.Equating the elements,we get $2x + 3 = x - 2$.Subtracting $x$ from both sides,we get $x + 3 = -2$.Subtracting $3$ from both sides,we get $x = -5$.Therefore,the correct value of $x$ is $-5$.

Class 12 Mathematics 3-4. Matrices and Determinants Special types of matrices, Transpose of matrices and Trace of matrices

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If $A = \begin{bmatrix} 5 & 2x+3 \\ x-2 & x+1 \end{bmatrix}$ is a symmetric matrix,then $x$ is equal to:

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A
$4$
B
$5$
C
$-5$
D
$-4$

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3-4. Matrices and Determinants

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Special types of matrices, Transpose of matrices and Trace of matrices

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