(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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

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