set of degree 2 polynomials a subspace

wumple

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!

Dick

Because f(0) isn't equal to 2 with a=0, b=0 and c=0. f(t) isn't in your set.

wumple

Oh, duh. thanks!