1. The problem statement, all variables and given/known data 3. The attempt at a solution I don't think I'm really understanding this problem. Let me tell you what I know: A set is linearly independent if [itex]a_1 A_1 +...+a_n A_n = \vec0[/itex] for [itex]a_1,...,a_n \in R[/itex] forces [itex]a_1 = ...=a_n = 0[/itex]. If [itex]f,g,h[/itex] take any of the [itex]x_i \in S[/itex], then one of the [itex]f,g,h[/itex] will map that element of S to zero, and no set containing [itex]\vec0[/itex] can be linearly independent. Somehow, however, I feel like I'm supposed to be arriving at the opposite conclusion.