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 17th, 2011, 10:02 AM   #1
Newbie
 
Joined: Nov 2011

Posts: 2
Thanks: 0

Vector spaces

Can you help me with this problem, please?

If these two operations are defined as follows. With these new definitions, is R3 a vector space?
a) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 2, y1 + y2 + 2, z1 + z2 + 2)
c(x, y, z)=(cx, cy, cz)

b) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 4, y1 + y2 + 4, z1 + z2 + 4)
c(x, y, z)=(cx + 4c 4, cy + 4c 4, cz + 4c 4)

Thanks!
bamby is offline  
 
November 18th, 2011, 10:19 AM   #2
Member
 
Joined: Jun 2010

Posts: 64
Thanks: 0

Re: Vector spaces

a) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 2, y1 + y2 + 2, z1 + z2 + 2)
c(x, y, z)=(cx, cy, cz)

b) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 4, y1 + y2 + 4, z1 + z2 + 4)
c(x, y, z)=(cx + 4c 4, cy + 4c 4, cz + 4c 4)

__________
With this operations the (R^3+) is not group
Suppose that (a,b,c) be the zero elemet then
(a,b,c)+(a,b,c)=(a,b,c) from this we have taht a+a+2=a then a=-2
similar we have zero element o=(-2,-2,-2),
By the other operation
if we have suppose that R^3 is vector space than we would have that for every c( get c=4)
c*0=0
for c=4
c*0=4(-2,-2,-2)=(-8,-8,-=(-2,-2,-2) absurde !!!

b) similary find the zero 0,
suppose 0=(x1,x2,x3) then 0+0=0
(x1, y1, z1)+(x1, y1, z1)=(x1 + x1 + 4, y1 + y1 + 4, z1 + z1 + 4)
we find x1=x2=x3=-4
for c=5 you will find that
c*(-4,-4,-4)=5*(-4,-4,-4)=(-4,-4,-4) if you calculate you will find "absurd".


So R^3 with thos operation can not form a vectorspace.
johnmath is offline  
November 21st, 2011, 07:47 AM   #3
Newbie
 
Joined: Nov 2011

Posts: 2
Thanks: 0

Re: Vector spaces

Thanks!
bamby is offline  
January 27th, 2014, 07:13 AM   #4
Newbie
 
Joined: Jan 2014

Posts: 2
Thanks: 0

Re: Vector spaces

Can you guys also help me with this problem, please?

If these two operations are defined as follows. With these new definitions, is R2 a vector space?
(x1, y1) + (x2, y2) = (x1, 0)
and c(x, y) = (cx, cy)
If the answer is no, can you list all axioms that fail.(I know there are 10 axioms)
Thanks you so much for your help
hahoangcao is offline  
January 30th, 2014, 06:41 AM   #5
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Vector spaces

You know there are 10 axioms? Do you know what those axioms are?

Can you not, yourself, check to see which of those axioms are true?
HallsofIvy is offline  
January 30th, 2014, 01:39 PM   #6
Senior Member
 
Joined: Mar 2012

Posts: 294
Thanks: 88

Re: Vector spaces

Is there ANY vector (a,b) in R^2 that will serve as the 0-vector under that operation?
Deveno is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
spaces, vector



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Vector Spaces anyone? alphaknight61 Linear Algebra 1 November 26th, 2012 04:54 AM
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.