Homework Statement
Let V = P_n(F), and let c_0, c_1,..., c_n be distinct scalars in F. For 0 <= i <= n, define f_i(p(x)) = p(c_i). Prove that {f_0, f_1,..., f_n} is a basis for V*. Hint: Apply any linear combination of this set that equals the zero transformation to p(x) =...