Results 1 to 2 of 2

Math Help - basis for kernel

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    142

    basis for kernel

    I know that a basis for the kernel is the map of the nullspace of the standard matrix for the linear transformation.

    I found the nullspace for a particular problem to have a basis formed by the set
    1/2
    -3
    -1/4
    1

    The original basis was the standard basis {1, x, x^2, x^3}.

    Because I am working with polynomials, my professor said that the basis for a kernel must be polynomials. How do I change the nullspace basis given above into a polynomial?
    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

    I found the nullspace for a particular problem to have a basis formed by the set
    1/2
    -3
    -1/4
    1

    The original basis was the standard basis {1, x, x^2, x^3}.

    Because I am working with polynomials, my professor said that the basis for a kernel must be polynomials. How do I change the nullspace basis given above into a polynomial?
    The matrix that you got is the coordinate vector. Meaning the coordinate vector relative to the ordered base:
    (1,x,x^2,x^3)
    That means the basis is,
    (1/2)(1)+-3(x)+(-1/4)(x^2)+1(x^3)
    Thus, the vector (polynomial in this case) is,
    \frac{1}{2}-3x-\frac{1}{4}x^2+x^3
    This is the basis for the nullspace.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Basis of kernel(T) where T is a linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: November 16th 2011, 01:42 PM
  2. Replies: 4
    Last Post: August 30th 2011, 05:48 PM
  3. Basis and co-ordinates with respect to a basis.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 5th 2010, 08:26 AM
  4. Basis image and kernel
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 4th 2010, 07:00 AM
  5. Replies: 3
    Last Post: February 11th 2009, 12:34 AM

Search Tags


/mathhelpforum @mathhelpforum