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Linear Transformation

  1. Apr 21, 2013 #1
    1. The problem statement, all variables and given/known data
    Define a Function T : P3 → ℝ3 by
    T(p) = [p(3), p'(1), 01 p(x) dx ]

    Show that T is a linear transformation

    2. Relevant equations
    From the definition of a linear transformation:
    f(v1 + v2) = f(v1) + f(v2)
    f(cv) = cf(v)

    3. The attempt at a solution
    This is how I've started the problem, but I'm not sure I'm heading in the right direction. Either way I'm stuck.

    T(p+q) = (p+q)(3), (p+q)'(1), ∫(p+q)(x)dx
    = p(3) + q(3), p'(1) + q'(1), ∫p(x)dx + ∫q(x)dx

    I'm not sure where to go from here. Thanks
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 21, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Just keep going. Does that = T(p)+T(q)? (And remember, those are definite integrals; no constants of integration there).
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