Hello everyone, it's final's time next week , so I will be posting here more often than usual Here is one problem I came across when doing review: The nullspace of non-zero 4x4 matrix cannot contain a set of 4 lin. indep. vectors. (T/F) The way I was thinking is that if I solve a homogeneous s-m with this matrix, and if the dimension of nullspace is 4, that means that there have to be 4 free variables in the homogeneous s-m, but matrix is just 4x4. And then there is this rank-nullity theorem that n = rank(A) + nullity(A), so in this case rank(A) = 0, is it ever possible? My guess is not. Does the same hold for dim of nullspace (nullity): it has to have at least one solution (trivial, where everyting = 0, but that does not mean that the nullity is an empty set!) ? Is it correct? Thanks in advance!