Show how the axioms for a vector space V can be used to prove the elementary properties
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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.
Fill in the missing axiom numbers in the following proof that 0u = 0 for every u in V .
Transcribed Image Text:
Ou = (0+ 0)u = Ou + Ou Add the negative of Ou to both sides: Ou + (-Ou) = [Ou + Ou] + (-Ou) Ou + (-Ou) = Ou + [Ou + (-Ou)] 0 = Ou + 0 0 = Ou by Axiom. by Axiom. by Axiom by Axiom. (a) (b) (c) - (d)
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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