Results 1 to 3 of 3

Math Help - Basis

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    158

    Basis

    what's the basis of the subspace of P spanned by
    x^2 - 1
    x^2 + 1
    4x
    2x-3


    and another basis question...

    what's the basis of the space of vectors in a plane with an equation of
    2x - 3y + 4z = 0
    Last edited by Noxide; October 20th 2009 at 01:08 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    678
    Thanks
    1
    Quote Originally Posted by Noxide View Post
    what's the basis of the subspace of P spanned by
    x^2 - 1
    x^2 + 1
    4x
    2x-3
    It will be a subspace of P2. (Polynomials of degree 2). i.e. dim <=3
    Check the above vectors for independence.


    and another basis question...

    what's the basis of the space of vectors in a plane with an equation of
    2x - 3y + 4z = 0
    What is the dim of the null-space? Substitute a few values you will ge the basis.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by Noxide View Post
    what's the basis of the subspace of P spanned by
    x^2 - 1
    x^2 + 1
    4x
    2x-3
    As said, just check for linear independence.

    In order to do that, use coordinated vectors and express for example x^2-1=(1,0,-1)_v or 4x=(0,4,0)_v and do the same for others and reduce the matrix to the echelon form, if one of the rows turns zero, then that vector makes the set linear dependent, so you just remove it to get your basis.


    Quote Originally Posted by Noxide View Post
    and another basis question...

    what's the basis of the space of vectors in a plane with an equation of
    2x - 3y + 4z = 0
    Write W=\{(x,y,z)\in\mathbb R^3:2x-3y+4z=0\} and make x,y or z (as you like) the subject of that condition, then put it in (x,y,z) and you'll find set wich generates the subspace, so again check for linear independence.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Basis of ker L --> Basis of vector space?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: September 17th 2011, 09:57 AM
  2. Replies: 4
    Last Post: August 30th 2011, 05:48 PM
  3. Basis and co-ordinates with respect to a basis.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 5th 2010, 08:26 AM
  4. How many different basis does this set contain?
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 27th 2010, 10:02 PM
  5. Basis
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 15th 2008, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum