CHAPTER 05.06: SYSTEM OF EQUATIONS: Rank of a matrix Example 1

 

 

In this segment we are take an example how to find the rank of a matrix. So letís suppose the problem statement is Ė hey - what is the rank of this particular matrix here 3, 1, 2, 2, 0, 5, 1, 2, 3. So right here you can see that itís a three by three matrix so the largest sub-matrix which Iím going to order of the sub-matrix, which Iím going to get by a three by three matrix will be a three by three so that itself tells me that rank of (A) is going to be less than or equal to 3. So it can be a maximum of 3 but it might be less than that; so how do we find out what is the rank of (A)? If I look at the determinant of (A), because the three by three matrix, and thatís the largest sub-matrix which I can find out of that the determinant of (A) itself is minus 23 and you can always figure out how to find the determinant of a matrix. So itís minus 23; so not equal to zero; so in this case the rank of the matrix the rank of (A) is just 3. And thatís the end of this segment.