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Orthogonal Basis

  1. Jul 9, 2011 #1
    Hi Everyone,
    I want to ask if I did this problem correctly.

    1. The problem statement, all variables and given/known data
    Find a orthogonal basis for subspace {[x y z]T|2x-y+z=0}


    2. Relevant equations
    X1= [3 2 -4]T, X2=[4 3 -5]T


    3. The attempt at a solution
    Gram-Schmidt:
    F1=X1= [3 2 -4]
    F2= X2- ((X2.F1)/||F1||2)F1= [4 3 -5]T + (26/29)[3 2 -4]T


    Thanks in advance.
     
  2. jcsd
  3. Jul 9, 2011 #2

    micromass

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    Hi hpayandah! :smile:

    I don't quite get how you obtained the 26 in the end. Could you explain? (Maybe I just miscalculated it).
     
  4. Jul 9, 2011 #3
    Hi, Thanks for replying, it's the result of:

    (X2 . F1) / (||F1||2)

    Attached is my work.
     

    Attached Files:

  5. Jul 9, 2011 #4

    micromass

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    Yes, that is correct. You wrote X2 wrong in the OP :smile:
     
  6. Jul 9, 2011 #5
    Appreciated.
     
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