Results 1 to 2 of 2

Thread: Kernel and range

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Kernel and range

    Give an example of a linear operator $\displaystyle L $on $\displaystyle M_{2x3}(F)$ such that $\displaystyle N(L) = R(L)$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    7
    Awards
    2
    Is it true that $\displaystyle M_{2\times 3}(F)$ is just the set of all $\displaystyle 2\times 3$ matrices over the field $\displaystyle F?$ And $\displaystyle N(L)$ is the kernel (the set of all vectors in the domain that get mapped to the zero vector in the range), and $\displaystyle R(L)$ is the range of $\displaystyle L?$ Because, if all of this is true, your problem is a trick question. It's impossible to answer, because the kernel is a subset of $\displaystyle F^{3},$ whereas the range is a subset of $\displaystyle F^{2}.$ I suppose you could think of the equals sign as a sort of embedding, but that's not very usual.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Kernel and range of a linear Transformation
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Jul 27th 2010, 04:35 AM
  2. Kernel and Range
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Mar 27th 2010, 01:45 PM
  3. Kernel and Range of Linear Transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Mar 29th 2009, 08:02 AM
  4. Kernel and Range of a linear operator
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Mar 7th 2009, 11:23 AM
  5. dim. Kernel & dim. Range
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Jan 30th 2008, 09:48 PM

Search Tags


/mathhelpforum @mathhelpforum