Basis for row space of matrix: REF vs. RREF. When finding a basis for the row space of a matrix, I reduce the matrix to row echelon form, and find the rows that have pivots in them. Does it matter wether you use the echelon or the reduced echelon form to find your row basis. If it matters, why?

No, that doesn't matter. In either case, the nonzero rows of the reduced matrix are clearly linearly independent, and the row operations you have used during the reduction do not change the row space. Therefore the nonzero rows of either the row echelon form or the reduced row echelon form will be a basis for the row space.
The basis that results from a reduced row echelon form will sometimes be easier to work with, but it's still a basis if you stop at the non-reduced form.
