# Math Help - Vector spaces

1. ## Vector spaces

Is the set of all polynomials over R of degree 2 a vector space over R ?

My book says, the answer is no. I can't understand why ? Isn't Pn (set of all polynomials with degree <= n with coefficients from F) a vector space over F .

2. ## Re: Vector spaces

Hint: the set of all polynomials of degree <= 2 is a vector space, but the set of all polynomials of degree exactly 2 is not.

3. ## Re: Vector spaces

Originally Posted by mrmaaza123
Is the set of all polynomials over R of degree 2 a vector space over R ?

You posted "of degree 2" not of degree $\le 2$. which is it?

4. ## Re: Vector spaces

Oh! right, Thank you. I got it now.

5. ## Re: Vector spaces

degree 2 doesn't include 0 vector so its not a vedtor space. <=2 includes 0.

Edit: also, degree 2 includes (0,0,1) but not (0,1,0) or (1,0,0)