Let V be the set of all continuous functions defined on [0,1].
Explain why V is a subspace of T(R).
Let W be the subset of V defined by W = {f E V: ∫(0 to 1) (f(t)dt = 0)}. Show that W is a subspace of V.
For the first part, it looks like I need to show:
1) zero vector of T(R) is in V
2) when u and v belong to V, u + v belongs to V
3) when u belongs to V and c is scalar, cu belongs to V
How would I show that the zero function lies in V?
Is it V(0) = 0?
I'm not sure what to do next.

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thanks, that makes sense

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