I don't know how to solve the following problem. Suppose that dim(V) = n and W = $\mathbb{R}$. The vectorspace V* = Hom(V, $\mathbb{R}$) is called the dual space of V. An element $\phi$ $\in$ V* is called a (linear) functional. Now, suppose that v, w $\in$ V such that $\phi$(v) = $\phi$(w) for all $\phi$ $\in$ V*. Can we conclude that v = w?
Thanks for your help.