Results 1 to 2 of 2

Math Help - show that P is a subspace..

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    87

    show that P is a subspace..

    Hey all, another subspace related question..

    how can I show that if P is a subspace of R^m, then U = \{\vec{u} \in R^n: A\vec{u} \in P\} is a subspace of R^n, where A is an m*n matrix.

    Thanks.
    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
    44

    Re: show that P is a subspace..

    (i) A0=0\in P (because P is subspace). Hence 0\in U.

    (ii) For all u,v\in U we have Au\in P and Av\in P. Then A(u+v)=Au+Av\in P (because P is subspace) . Hence u+v\in U .

    (iii) ... Try it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show a set is not a subspace of R^4
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 3rd 2011, 06:37 PM
  2. How to show that something is a subspace of something else?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 6th 2010, 06:52 AM
  3. Show something is a subspace..
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 17th 2009, 08:49 PM
  4. Show subspace Ua = span {a} is square on hyperplane H
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: September 22nd 2007, 06:53 AM
  5. How to show an eigenspace is a subspace of R^n
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 3rd 2006, 07:18 AM

Search Tags


/mathhelpforum @mathhelpforum