Solve the problem.
-Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether H is a vector space. If it is not a vector space, determine which of the following properties
It fails to satisfy.
A: Contains zero vector
B: Closed under vector addition
C: Closed under multiplication by scalars
A)H is not a vector space; not closed under multiplication by scalars
B)H is not a vector space; does not contain zero vector
C)H is a vector space.
D)H is not a vector space; not closed under vector addition

Question

Quizplus · Accepted Answer

H is not closed under multiplication by scalars because if p(x) is a polynomial in H and c is a rational number, then cp(x) may not be in H if c = 0.

Solve the Problem. -Let H Be the Set of All Polynomials Having Degree