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Math Help - Find the orthogonal complement

  1. #1
    Newbie
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    Mar 2010
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    Find the orthogonal complement

    Find the orthogonal complement W⊥ of W and give the basis for W⊥.


    {W=

    [x
    y ; x = t, y = -t, z = 3t}
    z]
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  2. #2
    Senior Member
    Joined
    Feb 2010
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    So you want the set of vectors orthogonal to (t,-t,3t). One vector orthogonal to this is (t,t,0). Another is the cross product of these two. Can you show that these two vectors span W⊥?
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