This is one of my linear algebra problems:
Prove that polynomials of degree $n$ does not (The professor made these words bold intentionally) form a vector space.
From what I read, the set of polynomials of degree $n$ should be a vector space, because:
- There is an "One" and a "Zero" in this set;
- We can find inverse for addition and multiplication from this set;
- It follows all the axioms of addition.
- It follows all the axioms of scalar multiplication.
Then can someone give me some hints to prove it does not form a vector space?