I am having difficulty with vector subspaces. It would be helpful if someone could give me an answer to at least one of these two questions.

1.

Prove that $\displaystyle W_1= \{(a_1,a_2· \cdot \cdot \cdot ,a_n) \in F^n : a_1+a_2\ + \cdot \cdot \cdot a_n =0 \} $ is a subspace of F^n, but $\displaystyle W_2= \{(a_1,a_2\,\cdot \cdot \cdot a_n) \in F^n : a_1+a_2 + \cdot \cdot \cdot a_n =1 \} $ is not

2.

Is the set W = { f(x) $\displaystyle \in $ P(F): f(x)=0 or f(x) has a degreen} a subspace of P(F) if n ≥ 1? Justify your answer