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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

    micromass

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    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

    micromass

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    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
    x1+2x2+3x3+4x4=0
    x2+x4=0

    x3 and x4 are my free variables

    setting x3=a
    x4=B

    We get x2=-B

    x1-2B+3a+4B=0

    x1=-2B-3a

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