Class 12Mathematics3 and 4 .Determinants and MatricesSpecial types of matrices, Transpose of matrices and Trace of matrices
EasyShow that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$ is a symmetric matrix.
(N/A) matrix $A$ is symmetric if $A^{\prime} = A$,where $A^{\prime}$ is the transpose of matrix $A$.
Given $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$.
To find the transpose $A^{\prime}$,we interchange the rows and columns of $A$:
$A^{\prime} = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$.
Since $A^{\prime} = A$,the matrix $A$ is a symmetric matrix.
Given $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$.
To find the transpose $A^{\prime}$,we interchange the rows and columns of $A$:
$A^{\prime} = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$.
Since $A^{\prime} = A$,the matrix $A$ is a symmetric matrix.
Explore More
Similar Questions
If $A$ and $B$ are symmetric matrices,prove that $AB - BA$ is a skew-symmetric matrix.
Medium
View SolutionSuppose $A$ and $B$ are two square matrices of the same order. If $A$ and $B$ are symmetric matrices, then $AB - BA$ is
If $A = \begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 5 \\ 2 & -5 & 0 \end{bmatrix}$,then
Easy
View SolutionFor any square matrix $A$,$AA^T$ is a
Medium
View SolutionIf $A$ is a skew symmetric matrix,then $A^{2021}$ is
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo