Results 1 to 2 of 2

Math Help - Find bases for the following subspaces of F^5

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    43

    Find bases for the following subspaces of F^5

    Find bases for the following subspaces of F^5:

    W1 = {(a1, a2, a3, a4, a5) E F^5 : a1 - a3 - a4 = 0}

    and

    W2 = {(a1, a2, a3, a4, a5) E F^5: a2 = a3 = a4 and a1 + a5 = 0}


    Well, I understand a basis is the maximum amount of vectors in a set that are linearly independent, or the smallest amount of L.I vectors that span a space. What is throwing me off is the constraints a1 - a3 - a4 = 0 and a2 = a3 = a4 and a1 + a5 = 0
    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
    Quote Originally Posted by zodiacbrave View Post
    Find bases for the following subspaces of F^5: W1 = {(a1, a2, a3, a4, a5) E F^5 : a1 - a3 - a4 = 0}

    Using a_1=a_3+a_4 express (a_1,a_2,a_3,a_4,a_5)\in W_1 as

    +a_3(\;\ldots\+a_4(\;\ldots\+a_5(\;\ldots\" alt="a_2(\;\ldots\+a_3(\;\ldots\+a_4(\;\ldots\+a_5(\;\ldots\" />

    Those four vectors span W_1 and it is easy to prove they are linearly independent.



    W2 = {(a1, a2, a3, a4, a5) E F^5: a2 = a3 = a4 and a1 + a5 = 0}

    Same method solving previously the system.


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Subspaces and Bases
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: May 10th 2011, 01:13 PM
  2. How do I find the bases for row(A), col(A) and null(A)?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 25th 2010, 11:27 PM
  3. subspaces and C-bases
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 18th 2009, 05:51 PM
  4. Find matrix for T for bases B and B'
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 31st 2009, 01:15 AM
  5. 2 subspaces of R^4, bases, intersection
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 15th 2009, 06:54 PM

Search Tags


/mathhelpforum @mathhelpforum