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 P_{2} such that the integral from 0 to 1 of p(x)dx=0}

Hint: A polynomial in P_{2} has the form ax^{2} + bx + c where a, b, c are elements of R and you will have to integrate.

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

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 $\displaystyle \frac{1}{3}a+\frac{1}{2}b+c=0$. With respect to the basis $\displaystyle \{x^2,x,1\}$, we have

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

Now do the same thing as I have shown you in the other question.