I'm studying for my exam on monday and i saw ap roblme that says: Determine if the following is a subspace of R^3. For it to be a subspace it has to pass 1) must have the zero vector 2) closure under addition 3) closure under multiplaication here is my work: http://img206.imageshack.us/img206/8067/lastscan1qn.jpg now it fails because it r1+r1-2 right? but why? because why wouldn't 3(s1+s2) also fail? because ur getting a different number if u like say, let s1 and s2 be 1, or r1 and 2 be 1, so did they both fail? Also if there was say What if there were only 2 variables, only r and s, and U = [r s r], r & s are in R, now would this automaticallya not be a subpsace in R^3?