Results 1 to 2 of 2

Thread: Transformation Proofs Help Please!!

  1. #1
    Jan 2010

    Transformation Proofs Help Please!!

    Hi, would someone be able to check my proofs for me and tell me if they are right and if not what is wrong please?

    So for the first one I said let u=p(x) and v=b(x)
    and T(ku)=(kp)(x)=kp(5)x^2=kTu
    So it is a linear transformation.

    For the second I said T(u+v)=p(x)+b(x)=x^2p(1/x)+x^2b(1/x)=Tp(x)+Tb(x)
    and T(ku)=x^2kp(1/x)=k(x^2p(1/x))=kTp(x)

    So it is also a linear transformation.
    For the third I said T(kp)(x)=xkp'(x)kp''(x)=k^2xp'(x)p''(x) which does not equal KTp(x)

    So it is not a linear transformation

    Did I do these right?

    Thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Jun 2009
    Your answers are essentially correct but your notation is wrong. What you should have written, for example for (a), is

    $\displaystyle T(p(x)+q(x)) = (p(5)+q(5))x^2 = p(5)x^2+q(5)x^2 = T(p(x))+T(q(x))$.

    It is not correct to write $\displaystyle T(u+v)=p(x)+q(x)$. Do you claim that $\displaystyle p(x)=p(5)x^2$? That makes no sense.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Need Help w/ Two Proofs.
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: Apr 8th 2011, 09:57 AM
  2. 2 proofs for unitary matrix/transformation prob.
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Feb 18th 2011, 02:20 AM
  3. Proofs, linear transformation is unitary
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: Aug 23rd 2010, 05:01 PM
  4. Proofs using ε
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 3rd 2010, 01:42 PM
  5. Replies: 3
    Last Post: Oct 6th 2007, 02:01 PM

Search Tags

/mathhelpforum @mathhelpforum