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

  1. 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. jcsd
  3. Defennder

    Defennder 2,616
    Homework Helper

  4. 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
     
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