## Romero Group Title Can a single vector with 4 terms span R^4? 2 years ago 2 years ago

1. UnkleRhaukus Group Title

you need a minimum of four vectors to span $$\mathcal{R} ^4$$

2. amistre64 Group Title

depends on your definition of span

3. UnkleRhaukus Group Title

oh,

4. amistre64 Group Title

can a single vector hit all of the points in R^4? No can a single vector stretch thru R^4? yes

5. UnkleRhaukus Group Title

a single vector of $$\mathbb{R}^4$$ is just a point, it has no span

6. Romero Group Title

so a vector with 4 terms is in R^4 right?

7. UnkleRhaukus Group Title

yeap, even if some of them are zero

8. Romero Group Title

gotcha ty

9. UnkleRhaukus Group Title

To span $$\mathbb{R}^4$$ you will need four linearly independent vectors in $$\mathbb{R}^4$$ such as $\left\{ \left( \begin{array} \\1\\0\\0\\0\end{array}\right), \left(\begin{array}\\0\\1\\0\\0\end{array}\right),\left(\begin{array}\\0\\0\\1\\0\end{array}\right),\left(\begin{array}\\0\\0\\0\\1\end{array}\right)\right\}$