Let V be the set of all ordered pairs of real numbers, and consider the following
Chapter 4, Problem 1(choose chapter or problem)
Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on and : (a) Compute and for , , and . (b) In words, explain why V is closed under addition and scalar multiplication. (c) Since the addition operation on V is the standard addition operation on , certain vector space axioms hold for V because they are known to hold for . Which axioms in Definition 1 of Section 4.1 are they? (d) Show that Axioms 7, 8, and 9 hold. (e) Show that Axiom 10 fails for the given operations.
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