1. Basis for row space

Hi, I hope someone can help provide further clarification on this theorem below. It seems that what it is saying is that while only the rows in the echelon form can create the basis for the row space, this basis will still be contained within the overall row space that A and B are both in. Is my thinking correct?

- otownsend

2. Re: Basis for row space

It's saying more than that. Not only are rows of B, in "reduced echelon form", in the row space of A, they are also a basis for that row space. If two matrices are "row equivalent" their row spaces are the same.

3. Re: Basis for row space

ok makes sense. Thanks!