Span and Spanning Sets

• If we have a set of vectors $B$.

• Then $\text{Span }B$ would be the set of all linear combinations of the vectors in $B$.

• To show that a vector $\vec{x}$ belongs in $\text{Span }B$, we must show that $\vec{x}$ can be expressed as a linear combination of vectors in $B$.

$$\begin{array}{r}\vec{x}\in \text{ Span}\{{\vec{v}}_1,...,{\vec{v}}_k\}\\ ⟹\vec{x}=c_1{\vec{v}}_1+...+c_n{\vec{v}}_n\end{array}$$

• $B$ is the spanning set for Span(B).