My Math Forum  

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

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
September 24th, 2012, 10:01 AM   #1
Joined: Sep 2012

Posts: 1
Thanks: 0

Abstract Algebra Help

1) Find two linear maps A,B: R2 ---> R2 such that AB ? BA

I understand how to find the two linear maps, but I am still lost with respect to "such that AB ? BA"

2) Let u and v be two linear independant vectors of a real vector space. Show that u + v and u - v are linearly independant. Is the same conclusion true if the vector space was over Z2.

For this one, I am just completely confused. I understand the idea of proving they are linearly independant but I am having trouble prooving if the same conclusion would be true over Z2.

Any help would be greatly appreciated.
MastersMath12 is offline  
September 24th, 2012, 11:07 PM   #2
Senior Member
Joined: Nov 2011

Posts: 595
Thanks: 16

Re: Abstract Algebra Help

For the first one, use for instance:
A: Rotation by 90 so (x,y)->(-y,x)
B: Translation by a vector u=(1,0) so (x,y)->(x+1,y)
You can check for instance taking an initial point xo=(1,0 ) AB(xo) is different than BA(xo)

Then for the second start with a(u+v)+b(u-v)=0. The aim is to show that a=b=0 then. You get (a+b)u+(a-b)v=0. Since u and v are independent this leads to a+b=0 and a-b=0. So a=b=0. I did also not understand what is the different if it is Z2 or R2 so probably check this again, perhaps I missed something there (or not)..
Dougy is offline  

  My Math Forum > College Math Forum > Abstract Algebra

abstract, algebra

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Books for Abstract Algebra eddybob123 Math Books 4 August 6th, 2013 08:44 PM
Abstract Algebra micle Algebra 1 June 17th, 2013 09:06 AM
Abstract Algebra Need Help ustus Abstract Algebra 4 October 14th, 2012 12:00 PM
Abstract Algebra forcesofodin Abstract Algebra 10 April 5th, 2010 10:31 PM
Abstract Algebra micle Abstract Algebra 0 December 31st, 1969 04:00 PM

Copyright © 2019 My Math Forum. All rights reserved.