Notation for Linear Algebra

Question

Considering $B$ a basis for a subspace $U$, is the notation below correct to describe any point $X \in U$?

$$ x = \sum_{i=1}^{dim(u)} \alpha_{i} \cdot V_{i} : \alpha_{i} \in R, V_{i} \in B $$

Answer 1

Just replace $B$ by span($B$) and the answer is yes.