Let Pn be the set of real polynomials of degree at most n. Show that S = {p ? P3 : p(-1) = p(3) = 0} is a subspace of P3. To check that you are on the right track, answer the following questions. • Is S a subset of a known vector space? Yes • Does S contain the zero element? Yes • Is S closed under vector addition? Yes • Is S closed under scalar multiplication? Yes
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