# span of a subset with polynomials

• Apr 4th 2013, 07:25 PM
widenerl194
span of a subset with polynomials

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.
• Apr 4th 2013, 07:27 PM
widenerl194
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
• Apr 4th 2013, 07:54 PM
Gusbob
Re: span of a subset with polynomials
Quote:

Originally Posted by widenerl194
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.