Results 1 to 2 of 2

Math Help - Kernel and Image

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    142

    Kernel and Image

    Let V be the R-space of real polynomials of degree at most 3.
    For p(X) in V, define

    Tp(X)=1/6(19-6x+7x^2+32x^3-15x^4-6x^5)p'''(X)+(6-7x-9x^2+5x^3+x^4)p''(X)+(7-5x^2+2x^3)p'(X)+(10-6x^2)p(X).

    I need to find a basis for each of the kernel ker(T) of T, and the image (or range) Im(T) of T (T is a linear operator on V).

    Any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by PvtBillPilgrim View Post
    Let V be the R-space of real polynomials of degree at most 3.
    For p(X) in V, define

    Tp(X)=1/6(19-6x+7x^2+32x^3-15x^4-6x^5)p'''(X)+(6-7x-9x^2+5x^3+x^4)p''(X)+(7-5x^2+2x^3)p'(X)+(10-6x^2)p(X).

    I need to find a basis for each of the kernel ker(T) of T, and the image (or range) Im(T) of T (T is a linear operator on V).

    Any ideas?
    After you find the standard matrix for the linear transformation does it not make sense to say that the kernel of the map of the nullspace of the standard matrix and the range of the map is the coloum space of the standard matrix? However, what that standard matrix is, I did not find it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Image and kernel
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: July 5th 2011, 04:26 PM
  2. Kernel and Image
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 11th 2011, 06:38 PM
  3. Image and Kernel
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: August 13th 2010, 05:36 AM
  4. Image and Kernel
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 23rd 2010, 09:36 PM
  5. Kernel and Image?
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: November 4th 2009, 07:58 AM

Search Tags


/mathhelpforum @mathhelpforum