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Math Help - Orthogonal decompostion

  1. #1
    Ife
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    Orthogonal decompostion

    ok so I am having a bit of difficulty expanding the answer to this question. since i can't type it out i found it online at this link: http://www.math.ust.hk/~macyfang/hw4.pdf

    it's question #2 under section 6.3.

    Now I know that I have to decompose v= v^ + z,

    but is v^ = (v.u1/u1.u1)x u1? I got v^ to be (2, 4, 2, 2) and z to be (2, 1, -5, 1)

    But i am wondering if this is correct, and if my calculation for v^ is correct..

    I am thinking that if {u1.... u4} is an orthogonal basis, then the span of {u2, u3, u4} is orthogonal to span {u1}.

    But for a 10 mark question, what have i left out??
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Your solution seems right. Why do you think it's wrong?

    Note that (2, 4, 2, 2) is indeed orthogonal to (2, 1, -5, 1).
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  3. #3
    Ife
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    my problem is that the working doesn't seem sufficient for the marks allotted for the question.. should there be more that I should add??
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by Ife View Post
    my problem is that the working doesn't seem sufficient for the marks allotted for the question.. should there be more that I should add??
    No, your solution is perfectly fine. (Don't worry about the marks alloted for a problem as long as you solve it correctly.)
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