Methods to Find Rank of a Matrix

What is Rank of a Matrix?

The rank of the matrix represents the number of non-zero rows and columns in the matrix.

What is the Rank of 3×3 Matrix?

If the determinant of 3×3 matrix is not zero than the rank of 3×3 matrix is 3 else, we have to find the rank using minors or Echelon form or normal form.

What is the Rank of Null Matrix?

The rank of null matrix is zero.

Can Rank of Matrix be More Than Number of Rows and Columns?

No, the rank of a matrix cannot be more than number of rows and columns.

How to Find Rank of a Matrix?

To find the rank of the matrix we can use one of the following ways:

• By Finding the minors of the matrix
• By using Echelon form

To find the rank of a matrix find the highest order of the non-zero minor within the matrix. Rank of a matrix in the number that represents the number of non-zeros rows or columns in the matrix. If the rank of the matrix is r then the matrix contains at least one minor with order r and the minors with order greater than r is zero. The second method to find the rank of matrix is by converting it into Echelon form.

In this article we will discuss methods to find rank of a matrix in depth along with the rank definition, methods to find rank of a matrix i.e., by minors and by Echelon form. Also, we will discuss the properties of rank and solve some examples including both the methods. Let’s start our learning on the topic “Methods to Find Rank of a Matrix. “