Question

Let �! be the vector space of all polynomials of degree ≤ 2. If W is the set of all polynomials of the
form �" + �#� + �!�! such that �" + 2�# + �! = 0 . Determine whether � is a subspace of �!.
Hint, � = {(�" + �#� + �!�!)|�" + 2�# + �! = 0}.

Answer 1

Answer:

Polynomials of degree n does not form a vector space because they don't form a set closed under addition.

Yes, any vector space has to contain 0, and 0 isn't a 2nd degree polynomial.

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