Exercises 25–29 show how the axioms for a
Chapter 4, Problem 25E(choose chapter or problem)
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.Complete the following proof that the zero vector is unique. Suppose that w in V has the property thatu + w = w + u = u for all u in V . In particular, 0 + w = 0.But 0 + w = w, by Axiom _______. Hence w = 0 + w = 0.
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