Question:
If $A = \begin{bmatrix}3&x-1\\ 2x+3&x+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is
If $A = \begin{bmatrix}3&x-1\\ 2x+3&x+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is
Updated On: Apr 27, 2024
- 4
- 3
- -4
- -3
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The Correct Option is C
Solution and Explanation
Since, $A$ is symmetric matrix, then $A=A'$
$\Rightarrow \begin{vmatrix}3 & x-1 \\ 2 x+3 & x+2\end{vmatrix}=\begin{vmatrix}3 & 2 x+3 \\ x-1 & x+2\end{vmatrix}$
$\Rightarrow x-1=2 x+3 \Rightarrow x=-4$
$\Rightarrow \begin{vmatrix}3 & x-1 \\ 2 x+3 & x+2\end{vmatrix}=\begin{vmatrix}3 & 2 x+3 \\ x-1 & x+2\end{vmatrix}$
$\Rightarrow x-1=2 x+3 \Rightarrow x=-4$
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.