Results 1 to 2 of 2

Math Help - Dimension and basis

  1. #1
    Newbie
    Joined
    Jan 2008
    Posts
    16

    Dimension and basis

    My text is not helping at all and the wikipedia explanations of the concepts: basis and dimension are way over my head.

    Let V be the space of polynomials in x and y of degree <= 10. Specify a basis of V and compute dimV.

    thanks

    jblorien
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    To be a basis it must span and be linearly independent.

    The polynomials 1,x,x^{2},x^{3},.....,x^{10} span the vector

    space of P_{n} since each p in P_{10} can be

    written as p=a_{0}+a_{1}x+....+a_{10}x^{10} which is a

    linear combination of S=\left[1,x,x^{2},.....,x^{10}\right].


    dim(P_{n})=n+1. The basis has n+1 vectors. In other words, it has dimension 11.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dimension and basis
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: November 12th 2011, 01:37 PM
  2. Basis and dimension
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 4th 2010, 12:02 AM
  3. Dimension and basis
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 17th 2009, 09:54 AM
  4. basis and dimension
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 25th 2008, 04:15 PM
  5. Basis and Dimension
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 22nd 2007, 10:03 PM

Search Tags


/mathhelpforum @mathhelpforum