Span

• The Set of all Linear Combinations of the $v$‘s in called the span of the $v$‘s
• e.g.

$$\text{span}(\left[\begin{array}{c}1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\end{array}\right])={\mathbb{R}}^2$$

• any 2 vectors in ${\mathbb{R}}^2$ that are not scalar multiplies of each other span ${\mathbb{R}}^2$ Q: Is $\vec{b}\in SPAN({\vec{a}}_1,{\vec{a}}_2)$

$$\vec{b}=\left[\begin{array}{c}7\\ 4\\ 3\end{array}\right],{\vec{a}}_1=\left[\begin{array}{c}1\\ -2\\ -5\end{array}\right],{\vec{a}}_2=\left[\begin{array}{c}2\\ 5\\ 6\end{array}\right]$$