Can a single vector with 4 terms span R^4?

Question

unklerhaukus · Answer

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

amistre64 · Answer

depends on your definition of span

unklerhaukus · Answer

oh,

amistre64 · Answer

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

unklerhaukus · Answer

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

anonymous · Answer

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

unklerhaukus · Answer

yeap, even if some of them are zero

anonymous · Answer

gotcha ty

unklerhaukus · Answer

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