Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Question

Find the orthogonal projection of $$x = \begin{bmatrix}7 \\ 0 \\ -4 \\ -4 \end{bmatrix}$$ onto the subspace of $\mathbb R^4$ spanned by $$v_1 = \begin{bmatrix}-4 \\ 2 \\ 2 \\ -4 \end{bmatrix}, v_2 =\begin{bmatrix}2 \\ 2 \\ 2 \\ 0 \end{bmatrix}$$

Answer

So I projected $x$ onto $v_1$ and $v_2$ and got $x_{v1} = \begin{bmatrix}2 \\ -1 \\ -1 \\ 2 \end{bmatrix} and, x_{v2} = \begin{bmatrix}1 \\ 1 \\ 1 \\ 0 \end{bmatrix}$ respectively.

I then subtracted $x_{v1}$ and $x_{v2}$ from $x$ and got $\begin{bmatrix}4 \\ 0 \\ -4 \\ -6 \end{bmatrix}$

which is wrong, and the correct answer should be $\begin{bmatrix}3 \\ 0 \\ 0 \\ 2 \end{bmatrix}$

So what have I done wrong?

share|improve this question
3  
Are you sure that you want to subtract these two things from $x$? Note that $x_{v1} + x_{v_2}$ is the expected answer. You seem to be calculating the component of $v$ which is orthogonal to the subspace in question. –  Dylan Moreland Apr 26 '12 at 0:35
    
Cheers mate, your right, i just got stuck in without properly reading the question. –  Jim_CS Apr 26 '12 at 0:37

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.