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 November 26th, 2012, 04:08 AM #1 Newbie   Joined: Nov 2012 Posts: 3 Thanks: 0 Vector Spaces anyone? Let V = Real Number. Define ? + ? = 2? -? and c(?) = c?. For example, 3+5=2(3)-5=1 and 3(5)=15. Is V a vector space or not? Support your answer. November 26th, 2012, 04:54 AM   #2
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Re: Vector Spaces anyone?

For it to be a vector space it must satisfy ALL the vector space axioms.

[attachment=0:1rpwmkpu]Vector space - Wikipedia, the free encyclopedia.png[/attachment:1rpwmkpu]

I will show you how it fails the first axiom, thereby disqualifying this particular relation being a vector space.

axiom 1) U + (V + W) = (U + V) + W

let U = 2 , V = 3 , W = 4

2 + (3 + 4) = 2 + [2(3) - 4] = 2 + (6-4) = 2 + 2 = 2(2) - 2 = 2

(2 + 3) + 4 = [2(2) -3] + 4 = (4 - 3) + 4 = 1 + 4 = 2(1) - 4 = -2

so the relation is not associative under the operation of addition, we didn't get the same result.

It actually fails 4 axioms, can you find the other 3? Attached Images Vector space - Wikipedia, the free encyclopedia.png (129.7 KB, 104 views) Tags spaces, vector Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post bamby Linear Algebra 5 January 30th, 2014 01:39 PM eraldcoil Abstract Algebra 2 March 20th, 2011 09:34 PM rayman Abstract Algebra 0 January 27th, 2011 08:35 AM remeday86 Linear Algebra 1 July 10th, 2010 04:20 AM al1850 Linear Algebra 1 March 20th, 2008 09:50 AM

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