My Math Forum Vector Spaces anyone?

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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?

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