(C) matrix $A$ is symmetric if $A = A^T$, where $A^T$ is the transpose of matrix $A$. Given $A = \begin{bmatrix} 3 & x-1 \\ 2x+3 & x+2 \end{bmatrix}$.

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(C) matrix $A$ is symmetric if $A = A^T$, where $A^T$ is the transpose of matrix $A$. Given $A = \begin{bmatrix} 3 & x-1 \\ 2x+3 & x+2 \end{bmatrix}$. The transpose $A^T$ is obtained by interchanging rows and columns: $A^T = \begin{bmatrix} 3 & 2x+3 \\ x-1 & x+2 \end{bmatrix}$. Since $A = A^T$, we equate the corresponding elements: $x-1 = 2x+3$. Subtracting $x$ from both sides: $-1 = x+3$. Subtracting $3$ from both sides: $x = -4$. Therefore, the value of $x$ is $-4$.

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

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If $A = \begin{bmatrix} 3 & x-1 \\ 2x+3 & x+2 \end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

WBJEE 2011 All WBJEE

A
$4$
B
$3$
C
-$4$
D
-$3$

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3 and 4 .Determinants and Matrices

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

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