Linear algebra orthogonal compliment

[Mdhiggenz]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[micromass]

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

 

[Jorriss]

Did you factor out the gamma's too?

 

[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.

 

[micromass]

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

 

[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)}