(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+

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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 and 4 .Determinants and Matrices Special types of matrices, Transpose of matrices and Trace of matrices

Easy

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

GSEB 2017 All GSEB

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

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

3 and 4 .Determinants and Matrices

Subtopic

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

Previous Year

GSEB 2017 Paper All GSEB years →

If $A$ and $B$ are symmetric matrices of the same order such that $AB+BA=X$ and $AB-BA=Y$,then $(XY)^{T}=$

MediumAP EAMCET 2022

View Solution

Find the transpose of the following matrix: $\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$

Easy

View Solution

If the matrix $A$ is both symmetric and skew-symmetric,then

Easy

View Solution

If $A$ is a square matrix and $A + A^T$ is a symmetric matrix,then $A - A^T$ is:

Easy

View Solution

Suppose $A$ and $B$ are two square matrices of the same order. If $A$ and $B$ are symmetric matrices, then $AB - BA$ is

EasyTS EAMCET 2016

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

If $A$ and $B$ are symmetric matrices of the same order such that $AB+BA=X$ and $AB-BA=Y$,then $(XY)^{T}=$

Find the transpose of the following matrix: $\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$

If the matrix $A$ is both symmetric and skew-symmetric,then

If $A$ is a square matrix and $A + A^T$ is a symmetric matrix,then $A - A^T$ is:

Suppose $A$ and $B$ are two square matrices of the same order. If $A$ and $B$ are symmetric matrices, then $AB - BA$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module