Let V=P_{n}(F) and let c_{0},c_{1},c_{2},...,c_{n} be distinct scalars in F.

a. For 0 \leq i \leq n, define f_{i} \in V^{*} by f_{i}(p(x)) = p(c_{i}) . Prove that  \{f_{0},f_{1},...,f_{n} \} is a basis for V^*

b. Show that there exist unique polynomials p_{0}(x),p_{1}(x),...,p_{n}(x) such that  p_{i}(c_{j}) = \delta _{ij} for  0 \leq i \leq n

I'm really lost in these problems, perhaps I don't have a good understanding of dual space, please help!