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Math Help - Linear Algebra Help - Question 0

  1. #1
    Junior Member
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    Linear Algebra Help - Question 0

    Hey guys!

    I just had some questions relating to orthogonality!

    10) Show that the given vectors form an orthogonal basis for R^2 or R^3.
    (Work is attached to file)

    12) Determine whether the given orthogonal set of vectors is orthonormal. If it is not, normalize the vectors to form an orthonormal set.
    (Need help on this one)
    [1/2] , [1/2]
    [1/2] [-1/2]
    Attached Thumbnails Attached Thumbnails Linear Algebra Help - Question 0-linear.jpg  
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  2. #2
    MHF Contributor

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    "Orthonormal" means TWO things:
    1) the vectors are orthogonal: their dot products are all 0. You checked that.

    2) The length of each vector is 1. I don't see where you checked that.

    For the other problem, are the two vectors orthogonal? Is their dot product 0? Is so are they of length 1? If not you can change a vectors length to 1 by dividing it by its length.
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