1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    Science Advisor
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear Transformation
  1. Linear Transformation (Replies: 1)

  2. Linear transformations (Replies: 4)

  3. Linear transformation (Replies: 4)

  4. Linear transformation (Replies: 18)

Loading...