Does the following set of vectors constitute a vector space? Assume \"standard\"

Question

Does the following set of vectors constitute a vector space? Assume "standard" definitions of the operations.

The set of all polynomials of degree two.

(1 pt) Does the following set of vectors constitute a vector space? Assume "standard" definitions of the operations. The set of all polynomials of degree two. A. Yes B. No If not, which condition(s) below does it fail? (Check all that apply) A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication C. There must be a zero vector | D. Every vector must have an additive inverse E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property l. Scalar multiplication must be associative J. None of the above, it is a vector space

Explanation / Answer

The set of all polynomials of degree two, denoted by P, (say) is not a vector space. The answer is No.

The zero vector has degree 0 and is not in P. Option C is the correct answer.

Note:

The set of all polynomials of degree less than or equal to two, denoted by P2 is a vector space.

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