Results 1 to 3 of 3

Math Help - Linear Transformation with matrixes

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    8

    Linear Transformation with matrixes

    Greetings , got stuck on the following queston
    Let M(3x3) be vector space of 3x3 matrices , let F : M(3x3) ---> M(3x3) be a linear transformation defined the following way :

    for every A in M(3x3) be F(A) = B is a symmetrice matrice

    F(A) = 1/2(A+A(T)) -1/3*Tr(A)*I
    Tr(B) = 0

    Find a basis for Ker F and Im F
    anyways while playing around with Ker F i found the way the matrix must look like for the Ker F


    also i think i got a basis for the ker F , but not sure how to go about with finding the Im F , also is my basis right ? here it is

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Yes, that's correct so far. Since the dimension of M(3x3) is 9 and the dimension of the kernel is 4, the rank-nullity theorem tells you that you're looking for a 5-dimensional range. But a symmetric 3x3 matrix with trace 0 must look like \begin{bmatrix}a&c&d\\c&b&e\\d&e&-a-b\end{bmatrix}.

    Now you do the rest!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    8
    I see , i mistakengly tried to find a matrix with the trace parts all being zero , so i got a 3 dimension each time , wich didnt go well with the dimV = dimkerf dim imf , but now i got it and solved it , thx for the help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 1st 2011, 10:00 PM
  2. Linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 13th 2011, 06:42 PM
  3. Linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 24th 2009, 05:40 PM
  4. Linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 27th 2009, 03:47 PM
  5. Linear Algebra.Linear Transformation.Help
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 5th 2009, 01:14 PM

Search Tags


/mathhelpforum @mathhelpforum