Find a basis for which contains a basis of , where
After row reduction
So I've found the basis for the image of A
How would I find the basis for which contains the image of A
EDIT: Ok so I've just seen the way my textbook does it, and they row reduce the matrix A alongside the identity matrix and then choose the columns from A and the identity matrix (which are the pivot columns in the reduced form).
Why does this method work?