(B) matrix $A = [a_{ij}]$ is called a skew-symmetric matrix if $A^T = -A$,which implies $a_{ij} = -a_{ji}$ for all $i, j$. For diagonal elements,we se

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

(B) matrix $A = [a_{ij}]$ is called a skew-symmetric matrix if $A^T = -A$,which implies $a_{ij} = -a_{ji}$ for all $i, j$. For diagonal elements,we set $i = j$,which gives $a_{ii} = -a_{ii}$. This implies $2a_{ii} = 0$,so $a_{ii} = 0$ for all $i$. Therefore,all diagonal elements of a skew-symmetric matrix are zero.

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

Medium

In a skew-symmetric matrix,the diagonal elements are all

A
Different from each other
B
Zero
C
One
D
None of these

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

If $P$ and $Q$ are symmetric matrices of the same order,then $PQ - QP$ is

EasyKCET 2019

View Solution

If $A = \begin{bmatrix} 3 & \sqrt{3} & 2 \\ 4 & 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & -1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,verify that $(A')' = A$.

Easy

View Solution

Find the transpose of the following matrix: $\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right]$.

Easy

View Solution

If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A + B = \begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}$,then $AB$ is equal to

DifficultJEE MAIN 2019

View Solution

If $A'$ and $B'$ are the transpose matrices of the square matrices $A$ and $B$ respectively,then $(AB)'$ is equal to:

Easy

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

In a skew-symmetric matrix,the diagonal elements are all

Similar Questions

If $P$ and $Q$ are symmetric matrices of the same order,then $PQ - QP$ is

If $A = \begin{bmatrix} 3 & \sqrt{3} & 2 \\ 4 & 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & -1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,verify that $(A')' = A$.

Find the transpose of the following matrix: $\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right]$.

If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A + B = \begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}$,then $AB$ is equal to

If $A'$ and $B'$ are the transpose matrices of the square matrices $A$ and $B$ respectively,then $(AB)'$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module