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Linear Transformation

  1. May 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Let V=<sinx,cosx> and T: V --> V be a transformation defined by T(f)=df/dx +f. Prove T is linear.

    3. The attempt at a solution

    T(f+g) = cosx-sinx+sinx+cosx
    T(f)+T(g) = (sinx+cosx)'+sinx+cosx
    = T(sinx)+T(cosx)

    T(αf)=αcosx +αsinx
    αT(f)= α(cosx+sinx)

    Since we proved both addition and scalar, we can conclude that T is linear.
  2. jcsd
  3. May 5, 2009 #2


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    Homework Helper

    I think you are supposed to take f and g to be any linear combination of sin(x) and cos(x). I.e. f(x)=a*sin(x)+b*cos(x), g(x)=c*sin(x)+d*cos(x). So you've got the right idea, but you are only doing special cases.
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