Results 1 to 3 of 3

Math Help - Prove that TU = T0

  1. #1
    Newbie Nona's Avatar
    Joined
    Oct 2009
    Posts
    23

    Prove that TU = T0

    Hello,
    I would like help in:
    Assume T and U are in L(V,V ) and that V = N(T)+N(U). Prove that TU = T0 . (T0 is the zero linear transformation)
    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Nona View Post
    Hello,
    I would like help in:
    Assume T and U are in L(V,V ) and that V = N(T)+N(U). Prove that TU = T0 . (T0 is the zero linear transformation)
    Thank you

    Let's see if I succeed in decoding the above: T,U are linear operators and N(T), N(U) are the corresponding null spaces, or kernel, of these operators.

    So, if V = N(T)+N(U) then  TU=T_0.

    Assuming I guessed correctly your symbols, the claim is false: as example take T,\,U\in L(\mathbb{R}^2,\mathbb{R}^2) , T\left(\begin{array}{c}x\\y\end{array}\right)=\lef  t(\begin{array}{c}x-y\\x-y\end{array}\right)\,,\,\,U\left(\begin{array}{c}x  \\y\end{array}\right)=\left(\begin{array}{c}0\\y\e  nd{array}\right)

    It's easy to check that \left(\begin{array}{c}a\\b\end{array}\right)=\left  (\begin{array}{c}b\\b\end{array}\right)+\left(\beg  in{array}{c}a-b\\0\end{array}\right)\in\,N(T)+N(U) , but TU\neq T_0 , as you can easily check.

    If by the above symbols you meant something else then the above is worthless (perhaps the above's worthless EVEN if I guessed correctly your symbols).

    Tonio
    Last edited by tonio; November 5th 2009 at 12:20 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie Nona's Avatar
    Joined
    Oct 2009
    Posts
    23
    Yes, you guessed write. And this is the question that I have to prove that TU=T_0.
    I wonder if Prof. quotation is to prove TU not equal T_0. maybe typo
    Thank you very much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 06:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 10:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 06:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 03:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 02:24 PM

Search Tags


/mathhelpforum @mathhelpforum