Ok from other posts, everyone seems to say that it doesn't matter if you stick vectors into a matrix via columns or rows. So i want to prove this to myself using an example from my notes. The only problem is, I get different answers. Can someone correct me? from my notes it says "show (0, 0,−5, 3), (4, 7,−1, 6), (0, 1, 2, 0) in R4 are linearly independent" So, down columns (and rearranging) -5,-1,2 0,4,0 0,7,1 3,6,0 which I can see is independent -5,-1,2 0,4,0 0,0,1 0,0,0 but that looks a lot like it belongs to R3, in my opinion.. Anyways, same thing rows instead, 4,7,-1,6 0,1,2,0 0,0,-5,3 Which looks like it's already in echelon form, to me. And also looks like its dependent because x3 = (some constant) x4. So something is wrong with what I'm doing, any help? Thanks.