@MichaelGreinecker I think there might be a subtle doubt here. So, I will add one more hint.
@MeAndMath Kind of correct, but a little incorrect too (in the sense that "Suppose you have only one known vector in your finite set, how will you make a linear combination?")
If $V$ is a vector space over $\mathbb{R}$, what is the set of all possible scalars?