I have just been studying Nullspaces... I want to make the following summary, will it be correct? C(A) is all possible linear combinations of the pivot columns of A. N(A) is all possible linear combinations of the free columns of A (if any exist). edit: I have a feeling these are insufficient as definitions, but I'll leave it as it is for now. edit2: I just realized that the second part could give the wrong dimensions for N(A).