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Math Help - Inner product/Projections

  1. #1
    Junior Member krtica's Avatar
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    Inner product/Projections

    Use the inner product





    in to find the orthogonal
    projection of onto the line spanned by .


    .



    Which is wrong.

    The projection of f onto L is given by f(x)-{g(x) dot f(x)/||g(x)||^2}*g(x)


    The inner product of g(x) and f(x) is
    (3 (-3)^2+6 (-3)+3) (2 (-3)^2-6 (-3)-9)+(3(0)^2 +6(0) +3)*(2(0)^2 -6(0) -9)+(3(3)^2 +6(3) +3)*(2(3)^2 -6(3) -9)= -135

    Inner product of g(x) with itself is then:
    (2(-3)^2 -6(-3) -9)*(2(-3)^2 -6(-3) -9)+(2(0)^2 -6(0) -9)*(2(0)^2 -6(0) -9)+(2(3)^2 -6(3) -9)*(2(3)^2 -6(3) -9) = 891

    -135/891 simplifies to -5/33

    Multiplying g(x) with -5/33 gives -(10 x^2)/33+(10 x)/11+15/11

    Subtracting this value from f(x) results with
    (109 x^2)/33+(56 x)/11+18/11, which is my final answer.


    I greatly appreciate your help!
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  2. #2
    Junior Member krtica's Avatar
    Joined
    Apr 2010
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    I'm also having difficulty with this question.


    Use the inner product in the vector space to find the orthogonal projection of onto the subspace spanned by and .
    (Caution: and do not form an orthogonal basis of .)


    I think I am going wrong because of minor miscalculations? My answer for this question is 5 x^2-5 x+5/6, which is incorrect.
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