Rank of a Matrix - Problem 3

3. Find the rank of 

Solution:

Given:

The order of matrix A is 3x3

Using the formula:  

The possible rank of matrix A is:

                                   

The highest possible sub-matrix of the given matrix is 3x3 order :

 Determinant of a 3x3 order is zero.

∴ The possible rank of matrix A is 

The possible 2x2 order sub-matrices of the given matrix are:  

Sub-matrices from 1st row and 2nd row by deleting the 3rd row:

Since, the determinant of at least one of the 2nd order sub-matrices formed from the 1st  and 2nd row is not equal to zero. 

Hence, the rank of matrix A  is 2 i.e., rank(A)=2