1. The problem statement, all variables and given/known data Which of the subsets of P2 given in exercises 1 through 5 are subspaces of P2? Find a basis for those that are subspaces. (P(t)|p(0) = 2) 2. Relevant equations 3. The attempt at a solution The solution manual says that this subset is not a subspace because it doesn't contain the function f(t) = 0 for all t. I thought the generic element is f(t) = a +bt + ct^2. Why doesn't the element with a = b = c = 0 count as a function f(t) = 0 for all t? I'm stumped. Thanks!