# Thread: -subspace -polynomial question upcoming exam soon!!

1. ## -subspace -polynomial question upcoming exam soon!!

Hi ,
I desperately need someones help with this question.
( please do not just say what do you think).I don't feel confident in subspaces yet.thanks.
F is a vector space of functions from R to R, with the usual operations of addition and scalar multiplication of functions. For the subset below of F, write down two functions that belong to the subset and determine whether or not the subset is a vector subspace of F.

The set of polynomials whose coefficients are all non-negative.

2. ## Re: -subspace -polynomial question upcoming exam soon!!

Originally Posted by n22
I don't feel confident in subspaces yet.thanks.
F is a vector space of functions from R to R, with the usual operations of addition and scalar multiplication of functions. For the subset below of F, write down two functions that belong to the subset and determine whether or not the subset is a vector subspace of F.
The set of polynomials whose coefficients are all non-negative.
If $g\in F$ is it necessitly true that $(-1)g\in F~?$ What would that tell you?

3. ## Re: -subspace -polynomial question upcoming exam soon!!

Originally Posted by Plato
If $g\in F$ is it necessitly true that $(-1)g\in F~?$ What would that tell you?
No it can not be a subspace of F because it has a negativve coefficient
Could you please think of one more example?

4. ## Re: -subspace -polynomial question upcoming exam soon!!

Originally Posted by n22
No it can not be an element of F because it has a negativve coefficient
Could you please think of one more example?
Well the point is that $F$ is not closed with respect to scalar multiplication. So it is not a subspace.