Determine if the given set is a subspace of set of prime numbers P 9ℙ9. Justify your answer. All polynomials of degree at most 99​, with positive real numberspositive real numbers as coefficients. Complete each statement below. The zero vector of set of prime numbers P 9ℙ9 is not in the set because zero is not aa positive real numberpositive real number. The set is closed under vector addition because the sum of two positive real numberspositive real numbers is aa positive real numberpositive real number. The set ▼ is is not closed under multiplication by scalars because the product of a scalar and aa positive real numberpositive real number ▼ is is not necessarily aa positive real numberpositive real number