Results 1 to 2 of 2

Math Help - Linear Algebra Subspace regarding linear map

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    Davis
    Posts
    22

    Linear Algebra Subspace regarding linear map

    Hi, i'm having trouble starting this proof and how to prove the ideas necessary.

    Let V and W be finite-dimensional vector spaces over F. Given T is in L(V,W), show that there is a subspace U of V such that the following are true:
    U(intersection)null(T)= {0} and range(T)={Tu:u in U}.

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member jakncoke's Avatar
    Joined
    May 2010
    Posts
    387
    Thanks
    80

    Re: Linear Algebra Subspace regarding linear map

    How about the linear map which takes every element of V to the 0 element of W. Then if you let U be the subspace with only the 0 element of V. then U \cap Ker(T) = U = {0} and Range(T) = 0 = {T*0, 0 \in {0} = U}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exam Tomorrow: Span vs. Subspace in Linear Algebra
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 13th 2012, 04:53 PM
  2. Exam Tomorrow: Span vs. Subspace Linear Algebra
    Posted in the New Users Forum
    Replies: 1
    Last Post: December 13th 2012, 03:03 PM
  3. linear algebra-dimension of subspace spanned by vectors
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 12th 2009, 08:49 AM
  4. linear algebra- vector-basis-subspace
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: October 10th 2008, 08:23 PM
  5. Linear algebra: Basis, Nullspace, Subspace
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 1st 2007, 10:33 PM

Search Tags


/mathhelpforum @mathhelpforum