In this segment we are take an example how
to find the rank of a matrix. So let’s suppose
the problem statement is 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
it’s a three by three matrix so the largest
sub-matrix which I’m going to order of the
sub-matrix which I’m 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 that’s 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 it’s minus
23 it's not equal to zero. So in this case the
rank of the matrix the rank of (A) is just
3. And that’s the end of this segment.
