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Romero

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

  • one year ago
  • one year ago

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

    • one year ago
  2. amistre64
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    depends on your definition of span

    • one year ago
  3. UnkleRhaukus
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    oh,

    • one year ago
  4. amistre64
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    can a single vector hit all of the points in R^4? No can a single vector stretch thru R^4? yes

    • one year ago
  5. UnkleRhaukus
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    a single vector of \(\mathbb{R}^4\) is just a point, it has no span

    • one year ago
  6. Romero
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    so a vector with 4 terms is in R^4 right?

    • one year ago
  7. UnkleRhaukus
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    yeap, even if some of them are zero

    • one year ago
  8. Romero
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    gotcha ty

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

    • one year ago
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