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Math Help - subsets U of the vector space V

  1. #1
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    subsets U of the vector space V

    How can I find the base and dim of U here?, V = P3; U = {p in P3 : p'(0) = p(1)}....now I've proven it is a subspace because it is closed under addition and scalar multiplication....but how can I find the base and dim?I was thinking about writing it as p(x)=a+bx+cx^2+dx^4=>p(x)'=b+2cx+3dx^2
    and...p'(0)=p(1)=>b=a+b+c+d=>d=-a-c....but what now?
    Thank you
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    p'(0)=p(1)\Leftrightarrow b=a+b+c+d \Leftrightarrow a+c+d=0

    Solving,

    \begin{bmatrix}{a}\\{b}\\{c}\\{d}\end{bmatrix}=\be  gin{bmatrix}{-c-d}\\{b}\\{c}\\{d}\end{bmatrix}=c\begin{bmatrix}{-1}\\{0}\\{1}\\{0}\end{bmatrix}+b\begin{bmatrix}{0}  \\{1}\\{0}\\{0}\end{bmatrix}+d\begin{bmatrix}{-1}\\{0}\\{0}\\{1}\end{bmatrix}

    Could you continue?


    Fernando Revilla
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  3. #3
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    yes..thank you
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