Table of Contents

## What is Symmetric and Skew Symmetric Matrix?

A symmetric matrix is a square matrix in which all the elements on the main diagonal are the same and all the other elements are the same as their counterparts on the diagonal below the main diagonal. A skew symmetric matrix is a square matrix in which all the elements on the main diagonal are the same and all the other elements are the same as their counterparts on the diagonal above the main diagonal.

## What is a Symmetric Matrix?

A symmetric matrix is a matrix that is equal to its own transpose.

## Skew Symmetric Matrix Definition

A skew symmetric matrix is a square matrix that is both skew symmetric and symmetric. A skew symmetric matrix is defined as a square matrix A such that

A = AT

where A is the skew symmetric matrix and T is the transpose of A.

## Transpose of a Matrix (AT)

The transpose of a matrix is a matrix that has the same number of rows and columns as the original matrix, but the order of the elements in each row is reversed.

## How to check Whether a Matrix is Symmetric or Not?

There are various ways to check whether a matrix is symmetric or not. One way is to check whether the matrix can be written as A = AT, where T is the transpose of A. If this is true, then the matrix is symmetric.

## Conditions for Symmetric and Skew Symmetric Matrix

A symmetric matrix is a square matrix in which all the elements on the main diagonal are the same and all the other elements are the same.

A skew symmetric matrix is a square matrix in which all the elements on the main diagonal are the same and the other elements are opposite of each other.

## How to check whether a Matrix is Skew Symmetric or not?

A Matrix is skew symmetric if the following equation is true for all i and j

Aij = -Aji

## Questions to solve

1. What is the volume of the rectangular prism?

The volume of the rectangular prism is 120 cm3.

## about Matrices:

In mathematics, a matrix is a rectangular array of numbers, symbols, or other mathematical objects. The numbers or objects in a matrix are called its elements or entries. The matrix with m rows and n columns is usually denoted by A = [a i,j ] where a i,j is the element at the intersection of the ith row and the jth column.

## Applications of Matrices:

1. Matrix operations are used in solving systems of linear equations.

2. Matrix operations are used in statistics to analyze data.

3. Matrix operations are used in physics to solve problems involving forces and motion.

4. Matrix operations are used in engineering to design structures and machines.

5. Matrix operations are used in economics to model financial systems.