07 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 $S$.

$$ \text{span}\{\vec{u}, \vec{v}\} = \{ c\vec{u}+d\vec{v}\; |\; c,d \in R \} $$

• 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.