Exercises 25–29 show how the axioms for a

Chapter 4, Problem 29E

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Exercises 25–29 show how the axioms for a vector space V can be used to prove the elementary properties described after the definition of a vector space. Fill in the blanks with the appropriate axiom numbers. Because of Axiom 2, Axioms 4 and 5 imply, respectively, that 0 + u = u and –u + u = 0 for all u.Prove that(-1)u = -u. [Hint: Show that u + (-1)u = 0.Use some axioms and the results of Exercises 27 and 26.]Exercises 27:Fill in the missing axiom numbers in the following proof that Exercises 26:Complete the following proof that –u is the unique vector in V such that u + (–u) = 0. Suppose that w satisfies u + w = 0. Adding –u to both sides, we have