Results 1 to 3 of 3

Math Help - Proving linear transformation maps 0 to 0

  1. #1
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Proving linear transformation maps 0 to 0

    Suppose that T : V -> W is linear. Prove that T(0) = 0.

    Not sure how I'm supposed to prove this. I know that transformations are supposed to preserve the zero vector, but I can never get my head around proving these things. I'm guessing it has something to do with preserving scalar multiplication and vector addition? What should I do?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Traveller's Avatar
    Joined
    Sep 2010
    Posts
    162

    Re: Proving linear transformation maps 0 to 0

    Hint: T(0) = T(0+0)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44

    Re: Proving linear transformation maps 0 to 0

    Another way: T(\vec{0})=T(0\cdot\vec{0})=\ldots .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 24th 2011, 05:11 AM
  2. Linear maps
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 10th 2010, 11:38 AM
  3. proving linear transformation in R^3
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 9th 2008, 05:40 PM
  4. Linear maps. Proving its linear, and describing kernal.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 20th 2008, 12:46 AM
  5. Help with proving for a basis and a linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 1st 2008, 03:12 AM

Search Tags


/mathhelpforum @mathhelpforum