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Homework Help: Linear algebra orthogonal compliment

  1. Apr 6, 2013 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 6, 2013 #2
    I have no idea what you're asking. Please provide more details.
  4. Apr 6, 2013 #3
    Did you factor out the gamma's too?
  5. Apr 6, 2013 #4
    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.
  6. Apr 6, 2013 #5
    I still have no idea what you mean with alpha's and beta's. Can you show me your work or your final solution?
  7. Apr 6, 2013 #6

    x3 and x4 are my free variables

    setting x3=a

    We get x2=-B



    basis would be {(-2B-3a)^T,-B^T,a^T,B)}
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