Why Use the Last Row of the Elimination Matrix for Left Nullspace?

[only_huce]

In class my professor row reduced a matrix A into the form U. Then he started to go over how to find the basis for the left nullspace in a matrix A.

Instead of going through the entire process of row reducing the transpose of A and finding its nullspace, he just used the last row of the elimination matrix E as the basis.

Can someone explain why this is so? Is it just a property of the leftnullspace? And can I use it for finding the basis of N(A^T) for any row reduced matrix?

 

[HallsofIvy]

No, that's not a general property. I suspect that this particular nullspace was one-dimensional and so could be spanned by a single vector. That is not generally true.