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Romero
 3 years ago
Can a single vector with 4 terms span R^4?
Romero
 3 years ago
Can a single vector with 4 terms span R^4?

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UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1you need a minimum of four vectors to span \( \mathcal{R} ^4\)

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0depends on your definition of span

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0can a single vector hit all of the points in R^4? No can a single vector stretch thru R^4? yes

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1a single vector of \(\mathbb{R}^4\) is just a point, it has no span

Romero
 3 years ago
Best ResponseYou've already chosen the best response.0so a vector with 4 terms is in R^4 right?

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1yeap, even if some of them are zero

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1To span \(\mathbb{R}^4\) you will need four linearly independent vectors in \(\mathbb{R}^4\) such as \[\left\{ \left( \begin{array} \\1\\0\\0\\0\end{array}\right), \left(\begin{array}\\0\\1\\0\\0\end{array}\right),\left(\begin{array}\\0\\0\\1\\0\end{array}\right),\left(\begin{array}\\0\\0\\0\\1\end{array}\right)\right\}\]
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