Vector Spaces, Subspaces and Polynomials.
I'm hoping this problem hasn't been posted before. I couldn't find a similar problem in the search so I'm posting a new thread.
Right, the following question was giving to us in one of our worksheets:
Now I know that, in order to prove that a certain vector space (V) is a subspace of another vector space (H), you have to go through the following three axioms:
Let V be the set of polynomials p(x) satisfying
Prove that V is a vector space by showing that it is a subspace of a larger vector space.
1) The zero vector of V is in H.
2) H is closed under vector addition.
3) H is closed under scalar multiplication.
The bit that's confusing me is the whole "integration" thing. I'm assuming the the range between -1 and 1 is reducing the size of the space of V... so am I supposed to integrate first or... I dunno, I just need general help with this problem.