# Homework Help: Difference between an orthogonal complement and the orthogonal complement's basis.

1. Dec 7, 2008

### bluewhistled

1. The problem statement, all variables and given/known data
I don't understand the difference between an orthogonal complement and it's basis. In this problem: W = [x,y,z]: 2x-y+3z=0 Find w's orthogonal complement and the basis for the orthogonal complement.

3. The attempt at a solution
I did a quick reduced row echelon to [2,-1,3] to get [1,-.5,1.5] and then found the nullspace which is [.5,1,0] and [-1.5,0,1] and this is either the orthogonal complement or the orthogonal complement's basis. Anyone know the difference?

2. Dec 7, 2008

3. Dec 7, 2008

### bluewhistled

Re: Difference between an orthogonal complement and the orthogonal complement's basis

I essentially answered my question before. My first one was getting convoluted with my posts. So I started a new one based on a different question. Would you mind deleting my original thread? And if you do, would you mind deleting your post claiming I started multiple threads so as not to discourage people from helping.

Thanks