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Math Help - span of a subset with polynomials

  1. #1
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    span of a subset with polynomials

    I'm not sure where to start with this one either

    Find a finite subset of each of the following subspaces for which the subspace is the span of the subset.

    {p(x) is an element of P2 such that the integral from 0 to 1 of p(x)dx=0}

    Hint: A polynomial in P2 has the form ax2 + bx + c where a, b, c are elements of R and you will have to integrate.
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  2. #2
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    Re: span of a subset with polynomials

    Is this the correct first step:

    Let ax^2 + bx + c be and element of W.
    Then the integral from 0 to 1 of ax^2 + bx + c = 0
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  3. #3
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    Re: span of a subset with polynomials

    Quote Originally Posted by widenerl194 View Post
    Is this the correct first step:

    Let ax^2 + bx + c be and element of W.
    Then the integral from 0 to 1 of ax^2 + bx + c = 0
    So \frac{1}{3}a+\frac{1}{2}b+c=0. With respect to the basis \{x^2,x,1\}, we have

    p(x)=\begin{bmatrix} a  \\ b \\c \end{bmatrix}=\begin{bmatrix} a  \\ b \\ -\frac{1}{3}a - \frac{1}{2}b \end{bmatrix}

    Now do the same thing as I have shown you in the other question.
    Last edited by Gusbob; April 4th 2013 at 08:05 PM.
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