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Projection on a subspace

  • Thread starter Dustinsfl
  • Start date
  • #1
699
5
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.
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
how about finding an orthogonal basis of S (orthonormal is even better), then the projection of x onto each basis vector...?
 
  • #3
lanedance
Homework Helper
3,304
2
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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