Question: Let P be the set all polynomials with real coefficients. a) Show that P is a vector space. b) Show that the set H =

Let P be the set all polynomials with real coefficients.

a) Show that P is a vector space.

b) Show that the set

H = {pP:p(t)=a+bt+ct2, where a, b, c are real numbers such that a+2b+3c=0} is a subspace of P.

c) Find the dimension of H.

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