My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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.
alphaknight61 is offline  
 
November 26th, 2012, 04:54 AM   #2
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

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
File Type: png Vector space - Wikipedia, the free encyclopedia.png (129.7 KB, 104 views)
agentredlum is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
spaces, vector



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Vector spaces bamby Linear Algebra 5 January 30th, 2014 01:39 PM
About Vector spaces, subspace :). eraldcoil Abstract Algebra 2 March 20th, 2011 09:34 PM
two vector spaces rayman Abstract Algebra 0 January 27th, 2011 08:35 AM
vector spaces remeday86 Linear Algebra 1 July 10th, 2010 04:20 AM
vector spaces al1850 Linear Algebra 1 March 20th, 2008 09:50 AM





Copyright © 2019 My Math Forum. All rights reserved.