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?