Ok, for anyone who has come across my problem via search, there are a few things that you need to know.
Span of vectors = subspace
p(t) = a0 + a1t1..+ a4t4
With p(0)=0 a0=0
W={a1t...a4t4
span = { t, t^2, t^3, t^4 }
Alright! I get that. However, what I don't get is the question. I see you listed a few polynomials as examples that satisfy vector 0 being an element of the subspace, but what is the question asking for? There is no polynomial or equation associated with the question.
I edited my original post for the first condition. I'm not sure how to check for p(x)=0 to lie in our subspace. I think I may be a bit confused by P_4(x). What does the P_4 mean?
Homework Statement
Let W = {p(t) ∈ P4(t): p(0)=0 }. Prove that W is a subspace of P4(t)Homework Equations
noneThe Attempt at a Solution
I know three things have to be true in order to be a subspace:
1. zero vector must exist as an element
2. if u and v are elements, u+v must be an element
3. if...