1. The problem statement, all variables and given/known data Let A be an mxn matrix. a. Prove that the set W of row vectors x in R^m such that xA=0 is a subspace of R^m. b. Prove that the subspace W in part a. and the column space of A are orthogonal compliments. 2. Relevant equations 3. The attempt at a solution a. to be a subspace, I believe i only need to show that W is closed under addition and multiplication. So I just show that (rx+sy)A=0. Right? b. Not too sure about this. Should I try to show that x dotted with a=0 for all x and a? Or should try to do something with the properties of orthogonal compliments? I can show that dim(W)= nullity(A), but I don't think that's really going to do anything for me.