# Homework Help: Projection on a subspace

1. Apr 5, 2010

### Dustinsfl

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

### lanedance

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

3. Apr 5, 2010

### lanedance

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