## Rank of a Matrix

The rank of a matrix is define in several ways. Here we will see most of all the definitions of the rank of a matrix and also we will discuss properties of the rank of a matrix. Rank of a Matrix Let $A$ be a non-zero matrix. A positive integer $r\in\mathbb{N}$ is called the rank …

## Elementary Column Operations on Matrices

Elementary row operations on matrices are used to solve system of linear equations. Here we will see elementary row operations with illustrations. Elementary Column Operations On Matrices There are three elementary column operations. Let us understand it one by one with example. Multiply a Column Through by a Nonzero Constant In this elementary column operation …

## Elementary Row Operations on Matrices

Elementary row operations on matrices are used to solve system of linear equations. Here we will see elementary row operations with illustrations. Elementary Row Operations on Matrices There are three elementary row operations. Let us understand it one by one with example. Multiply a Row Through by a Nonzero Constant In this elementary row operation …

## Symmetric and Skew Symmetric Matrices

Symmetric and Skew Symmetric Matrices The process of taking transpose of a matrix generally produce a new matrix but some times this new matrix is same as the original matrix or some times it may gives the negative of the original matrix. See the following examples. Examples of Transpose of Matrix: Transpose of a matrix …

## Transpose of Matrix

Transpose of the Matrix The transpose of a matrix is an important phenomenon in the matrix theory. Let us understand the concept of the transpose of a matrix. If I say roughly then the process of taking transpose of a matrix is something equivalent to changing the rows of the matrix into columns and columns …

## Algebra of matrices

Algebra of Matrices Algebra of matrices is a basic things to work with matrices. Algebra of matrices contains addition, subtraction, scalar multiplication and multiplication of matrices. Let us understand algebra of matrices in details with examples. Equal Matrices. Two matrices $A=[a_{ij}]$ and $B=[b_{ij}]$ are called equal matrices if Number of rows of $A=$ Number of …

## Introduction to matrices

Introduction to Matrices In broad sense the meaning of a matrix is an arrangement of things; things may be books or people or tasks or price or names or numbers etc. The Sudoku block is an example of a matrix. In Mathematics generally entries in matrices are numerical values. There are huge number of applications …