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 Exercise [13.02] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [13.02]
Let V be a vector space.Then,
1.V is closed under vector addition.(The sum of two vectors is again a vector.)
2.For any two vectors \xi and \eta in V we have by definition,
\xi +\eta=\eta +\xi(Commutativity)
3.For any three \xi,\eta and \zeta in V,we again have by definition
\xi +(\eta +\zeta)=(\xi +\eta) +\zeta(Associativity)
4.There exists a null vector such that,
0+\xi=\xi + 0=\xi for all \xi in V.(Existence of identity)
5.There exists a 'negative' vector -\xifor any \xi in V such that,
-\xi +\xi=\xi +(-\xi)=0(Existence of inverse)
Thus,V satisfies all the requirements of an abelian group.

24 Aug 2008, 10:11
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