anonymous
  • anonymous
Can a single vector with 4 terms span R^4?
Mathematics
schrodinger
  • schrodinger
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UnkleRhaukus
  • UnkleRhaukus
you need a minimum of four vectors to span \( \mathcal{R} ^4\)
amistre64
  • amistre64
depends on your definition of span
UnkleRhaukus
  • UnkleRhaukus
oh,

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amistre64
  • amistre64
can a single vector hit all of the points in R^4? No can a single vector stretch thru R^4? yes
UnkleRhaukus
  • UnkleRhaukus
a single vector of \(\mathbb{R}^4\) is just a point, it has no span
anonymous
  • anonymous
so a vector with 4 terms is in R^4 right?
UnkleRhaukus
  • UnkleRhaukus
yeap, even if some of them are zero
anonymous
  • anonymous
gotcha ty
UnkleRhaukus
  • UnkleRhaukus
To span \(\mathbb{R}^4\) you will need four linearly independent vectors in \(\mathbb{R}^4\) such as \[\left\{ \left( \begin{array} \\1\\0\\0\\0\end{array}\right), \left(\begin{array}\\0\\1\\0\\0\end{array}\right),\left(\begin{array}\\0\\0\\1\\0\end{array}\right),\left(\begin{array}\\0\\0\\0\\1\end{array}\right)\right\}\]

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