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Math Help - orthogonal basis

  1. #1
    Member akhayoon's Avatar
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    orthogonal basis

    U=span{[1 -2 1 -1], [ 2 1 -1 1]}. show that Y=[1 3 -2 2] is in U, and find all Z such that [Y,Z] is an orthogonal basis of U.

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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by akhayoon View Post
    U=span{[1 -2 1 -1], [ 2 1 -1 1]}. show that Y=[1 3 -2 2] is in U, and find all Z such that [Y,Z] is an orthogonal basis of U.

    Y = [2 1 -1 1] - [1 -2 1 -1]
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  3. #3
    Member akhayoon's Avatar
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    well, thanks but...what about the rest?
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  4. #4
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    Y = [2 1 -1 1] - [1 -2 1 -1]
    Notice that {[1 -2 1 -1], [ 2 1 -1 1]} is an orthogonal basis for U.
    Writing Y with respect to this basis is (-1,1)
    so (-1,1) \bullet Z = 0
    so Z can be span{(1,1)}
    so Z can be span {(3,-1,0,0)}
    Last edited by badgerigar; December 12th 2007 at 04:07 AM. Reason: forgot math tags
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  5. #5
    Member akhayoon's Avatar
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    so you're proving that Z is orthogonal using the dot product?
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  6. #6
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    I think you need to revise the definition of orthogonal.
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