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Romero

  • 2 years ago

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

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

  2. amistre64
    • 2 years ago
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    depends on your definition of span

  3. UnkleRhaukus
    • 2 years ago
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    oh,

  4. amistre64
    • 2 years ago
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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

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

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

  7. UnkleRhaukus
    • 2 years ago
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    yeap, even if some of them are zero

  8. Romero
    • 2 years ago
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    gotcha ty

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

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