- #1

mattTch

- 2

- 0

- TL;DR Summary
- Let A be an m×n matrix. I am not sure why it's immediately obvious that the set B containing all and only the column vectors of R = RREF(A) which have leading ones, forms a basis for R. In particular, why is it the case that Span(B) = Col(R)? FYI: The linear independence of B is obvious to me.

Theorem: The columns of A which correspond to leading ones in the reduced row echelon form of A form a basis for Col(A). Moreover, dimCol(A)=rank(A).