Rank of a Matrix - Problem 4 & 5

4. Find the rank of 

Solution:

Given:

The order of matrix A is 4x3

Using the formula:   

The possible rank of matrix A is:

                                  

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

 Since, the determinant of at least one of the 3rd order sub-matrices is not equal to zero. 

Hence, the rank of matrix A is 3 i.e., rank(A)=3 

5. Find the rank of

Solution:

Since all the elements in the given matrix are zero i.e., it is a null matrix or a zero matrix.

Hence, the rank of the given matrix is 0 i.e., rank(O)= 0.

NOTE: Only a null/zero matrix has rank zero.