Question

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

Answer 1

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

Answer 2

depends on your definition of span

Answer 3

oh,

Answer 4

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

can a single vector stretch thru R^4? yes

Answer 5

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

Answer 6

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

Answer 7

yeap, even if some of them are zero

Answer 8

gotcha ty

Answer 9

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