# 08 Span

If $S=\{\vec{v}_{1}, \vec{v}_{2}, \dots, \vec{v}_{k}\}$ is a set of vectors, then the * span* of $S$, denoted by $\text{span}\{S\}$. is the set of all possible linear combinations of the vectors in $S$.

- Asking whether a vector is in the span of some other vectors is the same as asking if it is in the span of those other vectors.