Results 1 to 4 of 4

Math Help - Finding the Kernel

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    150

    Finding the Kernel

    Please note: This question does not count for my grade. It comes from a final study guide. Can someone please verify I did it (part d) correctly? Thanks!





    Attempt at Solution:

    (a1+1)+(a2+2)t=0

    This gives the system:

    a1+1=0
    a2+2=0

    So,

    a1=-1
    a2=-2

    So the set of all vectors for which L(a1,a2)=0 is:
    N(L)={(a1,a2)|a1=-1 and a2=-2}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Finding the Kernel

    Quote Originally Posted by divinelogos View Post
    So the set of all vectors for which L(a1,a2)=0 is:
    N(L)={(a1,a2)|a1=-1 and a2=-2}
    Right, and from (a), \vec{0}_V=(-1,-2) so N(L)=\{\;\vec{0}_V\} .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2010
    Posts
    150

    Re: Finding the Kernel

    And therefore the transformation is one-to-one?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Finding the Kernel

    Quote Originally Posted by divinelogos View Post
    And therefore the transformation is one-to-one?
    Yes, for that reason is injective.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: January 4th 2012, 12:05 AM
  2. Finding a Linear Transformation given its Kernel
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: February 2nd 2011, 11:06 PM
  3. Kernel
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 5th 2010, 03:15 AM
  4. Kernel
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 19th 2009, 06:38 AM
  5. Finding the Kernel for a Transformation matrix
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: October 29th 2008, 11:43 PM

Search Tags


/mathhelpforum @mathhelpforum