Linear Algebra questions (vector spaces)

[pulpfiction]

Hello.. I'm studying for my linear alg. final, and came across a few problems that I'm not sure how to do. Here goes:

Determine whether the following sets are subspaces. Justify your answer using a definition/theorem:

1. H={(a+b), 2, (2a-b)}, where a and b are real numbers



2. H= {(a+3b), (a-b), (2a+b), (4a)}, where a and b are real numbers


Also,
Consider the following subset of P2: H=P(t)=at^2, a>=0:
(a) Show that 0 is a member of H
(b) Show that H is closed under addition.
(c) Find a particular example to show that H is not closed under scalar multiplication.


Thanks for your help!