Basis of Orthogonal Complement

  1. Let S be the subspace of R^3 spanned by x=(1,-1,1)^T.

    Find a basis for the orthogonal complement of S.

    I don't even know where to start... I would appreciate your help!
     
  2. jcsd
  3. Dick

    Dick 25,887
    Science Advisor
    Homework Helper

    If (a,b,c)^T is a general vector in R^3 then it's orthogonal to (1,-1,1)^T if the dot product is zero. What conditions does that give you on a, b and c?
     
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