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Homework Help: Projection on a subspace

  1. Apr 5, 2010 #1
    Let S be a subspace of R3 spanned by u2=[tex]\left[ \begin{array} {c}
    \frac{2}{3} \\
    \frac{2}{3} \\
    \frac{1}{3} \end{array} \right][/tex] and u3=[tex]\left[ \begin{array} {c}
    \frac{1}{\sqrt{2}} \\
    \frac{-1}{\sqrt{2}} \\
    0 \end{array} \right][/tex].
    Let x=[tex]\left[ \begin{array} {c}
    1 \\
    2 \\
    2 \end{array} \right][/tex]. Find the projection of p of x onto S.

    I know how to find projection but I am not sure about doing the projection on a subspace.
     
  2. jcsd
  3. Apr 5, 2010 #2

    lanedance

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    how about finding an orthogonal basis of S (orthonormal is even better), then the projection of x onto each basis vector...?
     
  4. Apr 5, 2010 #3

    lanedance

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    or equivalently, S represents a plane in [itex]\mathbb{R}^3[/itex], so find the projection of X on that plane...
     
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