1. Consider the set V of all polynomials of degree two or less, along with the following definitions of addition and scalar multiplication: (azx? + a,x + a,) + (bzx? + b,x + bo) = (a, + bo)x? + (a, + b,)x+ (ao + bo) k(azx? + a,x + ao) = ka,x? + ka,x + kaz a. Is Vector Space Axiom 7, k(ü + v) = kū + kö satisfied? Support your answer appropriately. b. Would 0 0x2 + 0x +0 be the zero vector used to verify Axiom 4, ü +0 =0+ ü ? Explain. c. Given your answer to part b, is it possible to verify Axiom 5, u+-ü = -u+u = 0 ? If yes, define-ū and verify the axiom. If no, explain why. %3D %3D

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