Results 1 to 2 of 2

Math Help - Subspace proof

  1. #1
    Junior Member
    Joined
    Apr 2012
    From
    New York
    Posts
    30

    Subspace proof

    Let U be the set of symmetric 2 x 2 matrices. Prove that U is a subspace of the vector space of all 2 x 2 matrices; Find a "standard basis" for U and the dimension of U.

    Any help with this would be much appreciated!


    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87

    Re: Subspace proof

    To see that U is a subspace of M_n(\mathbb{R}) (or M_n(\mathbb{C})), check that: the zero matrix is symmetric, the sum of two symmetric matrices are symmetric, and that the multiplication of a symmetric by a scalar is still symmetric.

    I'm afraid I can't give a hint for a basis without giving away the answer. You have to think about this one yourself, but it is not hard to see what is has to be.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Subspace proof
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 14th 2010, 10:26 PM
  2. Subspace proof
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: November 25th 2010, 01:02 PM
  3. subspace proof
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 6th 2009, 10:11 AM
  4. subspace proof
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 1st 2009, 12:18 PM
  5. Need a proof for a subspace
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 5th 2009, 03:47 PM

Search Tags


/mathhelpforum @mathhelpforum