Rank of a matrix: Example 1

Rank of a matrix: Example 1


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.

24 COMMENTS

    What about a 3*6 matrix…if one submatrix has det. Zero and other has det. Non zero…which case will we take?

    You people are good for research maybe, but for academia please stay out of it. Give us your job we will do it much better than you.P.S. My research guide is like this.

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