Is there a linear algebra theorem or fact that says something like For a linear transformation T:Rn -> Rm and its standard m x n matrix A: (a) If the columns of A span Rn the transformation is onto. (b) If the columns of A are linearly independent the transformation is one-to-one. Is this correct? I can't find it anywhere in my textbook but it may have been mentioned in lecture. Any insight would be appreciated.