Determine whether or not the following subset is a subspace of the given real vector space.

{p(x) is an element of P : the integral from 0 to 1 of p(x) dx=0}

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- Mar 19th 2013, 08:04 PMwidenerl194Subspaces
Determine whether or not the following subset is a subspace of the given real vector space.

{p(x) is an element of P : the integral from 0 to 1 of p(x) dx=0} - Mar 19th 2013, 09:34 PMchiroRe: Subspaces
Hey widenerl194.

Hint: First try stating the subspace axioms. You need the zero vector for a start: Can you prove the zero vector lies in the sub-space? - Mar 21st 2013, 12:23 PMwidenerl194Re: Subspaces
So for that would I put:

zero vector = p(0) in P as the integral from 0 to 1 p(0) dx = 0

I really don't know what I'm doing here - Mar 21st 2013, 12:58 PMPlatoRe: Subspaces
- Mar 21st 2013, 02:30 PMwidenerl194Re: Subspaces
A subset of V is a subspace of V provided it is a real vector space (?) under the same addition and scalar multiplication as that of V.

- Mar 21st 2013, 02:39 PMPlatoRe: Subspaces
- Mar 21st 2013, 05:45 PMwidenerl194Re: Subspaces
I know the first is true. But I feel like the second one isn't

- Mar 21st 2013, 05:46 PMwidenerl194Re: Subspaces
And if only one of those is true then the subset is not a subspace

- Mar 21st 2013, 06:01 PMPlatoRe: Subspacesd
- Mar 21st 2013, 06:17 PMwidenerl194Re: Subspaces
This is help forum... and calculus isn't exactly easy. There's no need to be rude when I'm only asking for help. I said at the beginning that I didn't know what I was doing.

- Mar 21st 2013, 08:11 PMPlatoRe: Subspaces
- Mar 21st 2013, 08:32 PMwidenerl194Re: Subspaces
If I didn't have to do it, I wouldn't be posting on this forum. There aren't choices on homework assignments.