0

I have already read this link Prove: The set of all polynomials p with p(2) = p(3) is a vector space But am still confused. I understand that there is a zero vector in this set as 2P(0)-P(1)=0, but how do I prove closed addition? This is what I attempted:

2P(0)-P(1)=0 and (2P(0)-P(1))-(2P(0)-P(1)=0 therefore is is a vector space. This kind of makes sense to me but I am unsure if I am understanding the concepts correctly.

Could someone also give me an example of a subset that is not a vector space because it does not have a zero vector in it?

physicsgal
  • 1
  • For your last question consider the subset $P_0$ of $P$ such that $p(0)=2$ for all $p \in P_0$. – Paul Sep 27 '17 at 16:59
  • For the last question: ${ p \in P : p(0) = 1 }$. (And an example where zero is in the subset but it's not closed under addition: ${ p \in P : p(2) = p(0) p(1) }$.) – Daniel Schepler Sep 27 '17 at 16:59

0 Answers0