Results 1 to 3 of 3

Math Help - basis for polynomials

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    142

    basis for polynomials

    I have B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1) and C=(1+x^2, 1+x+2x^2, 1+4x+5x^2+x^3, -2+2x-x^2+5x^3).

    Also, p(x)=3-8x+2x^2-6x^3.

    I need to find [p]subscriptB and [p]subscriptC. What is it?

    I'm really confused by my notes and nothing seems to work.
    I need to show that the change of basis matrix from C to B times [p]subB=[p]subC and it doesn't work. I know the change of basis matrices.

    Any help greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2006
    Posts
    142
    Basically, what's the equation/formula for [p]subscriptB?

    Here's my work for finding [p]subscript B:
    I have the equation p(x)=3-8x+2x^2-6x^3 and B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1).
    I said a(1+x+x^2+x^3)+b(1+x+x^2)+c(1+x)+d=3-8x+2x^2-6x^3.
    I solved for a,b,c,d and got:
    a=-6
    b+a=2
    a+b+c=-8
    a+b+c+d=3

    Thus, a=-6, b=8, c=-10, d=11.

    So I said that [p]subscriptB is the vector:
    [-6
    8
    -10
    11]
    , but this is obviously not right.

    Any help or guidance would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by PvtBillPilgrim View Post
    Basically, what's the equation/formula for [p]subscriptB?

    Here's my work for finding [p]subscript B:
    I have the equation p(x)=3-8x+2x^2-6x^3 and B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1).
    I said a(1+x+x^2+x^3)+b(1+x+x^2)+c(1+x)+d=3-8x+2x^2-6x^3.
    I solved for a,b,c,d and got:
    a=-6
    b+a=2
    a+b+c=-8
    a+b+c+d=3

    Thus, a=-6, b=8, c=-10, d=11.

    So I said that [p]subscriptB is the vector:
    [-6
    8
    -10
    11]
    , but this is obviously not right.
    Why is this obviously not right? It looks OK to me.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum of Lagrange Basis Polynomials is 1
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: September 26th 2011, 10:38 AM
  2. Basis of ker L --> Basis of vector space?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: September 17th 2011, 09:57 AM
  3. Replies: 4
    Last Post: August 30th 2011, 05:48 PM
  4. How does one find a basis for a set of polynomials?
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 23rd 2010, 12:19 PM
  5. Grobner Basis and roots of polynomials
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 22nd 2008, 10:45 PM

Search Tags


/mathhelpforum @mathhelpforum