# Linear algebra orthogonal compliment

1. Apr 6, 2013

### Mdhiggenz

1. The problem statement, all variables and given/known data

Hello, I took my quiz today, and had to find a basis for an orthogonal compliment,

would it be incorrect to not factor out the alphas and betas?

2. Relevant equations

3. The attempt at a solution

2. Apr 6, 2013

### micromass

Staff Emeritus
I have no idea what you're asking. Please provide more details.

3. Apr 6, 2013

### Jorriss

Did you factor out the gamma's too?

4. Apr 6, 2013

### Mdhiggenz

With pleasure.

Let S be the subspace of R4
spanned by x = (1;2;3;4)T
and y = (0;1;0;1)T

Find a basis of S orthogonal compliment

So I found the correct basis however I did not factor out the alpha's and betas. Since we had free variables.

5. Apr 6, 2013

### micromass

Staff Emeritus
I still have no idea what you mean with alpha's and beta's. Can you show me your work or your final solution?

6. Apr 6, 2013

### Mdhiggenz

x1+2x2+3x3+4x4=0
x2+x4=0

x3 and x4 are my free variables

setting x3=a
x4=B

We get x2=-B

x1-2B+3a+4B=0

x1=-2B-3a

basis would be {(-2B-3a)^T,-B^T,a^T,B)}