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Math Help - Linear Algebra Linear transformations Vector spaces

  1. #1
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    Linear Algebra Linear transformations Vector spaces

    Really stuck on this problem please help.

    Let V be the vector space over R spanned by the functions,
    e0(x)=1, e1=sin(x), e2(x)=cos(x), e3=sin(2x), e4(x)=cos(2x)

    Furthermore consider the map D:V->V, f->df/dx,
    where df/dx denotes the derivatives of f.

    (a)Show that D is a linear transformation and determine the kernel ker(D) as well as the image imD.
    (b)Show that the set {e0,e1,e2,e3,e4} is a basis for V.
    (c)Determine a matrix representation of the linear transformation D.
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  2. #2
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    Re: Linear Algebra Linear transformations Vector spaces

    How about you start by showing that D is a linear transformation?
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