My Math Forum Abstract Algebra Help

 Abstract Algebra Abstract Algebra Math Forum

 September 24th, 2012, 10:01 AM #1 Newbie   Joined: Sep 2012 Posts: 1 Thanks: 0 Abstract Algebra Help 1) Find two linear maps A,B: R2 ---> R2 such that A°B ? B°A I understand how to find the two linear maps, but I am still lost with respect to "such that A°B ? B°A" 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.
 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 ) A°B(xo) is different than B°A(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)..

 Tags abstract, algebra

 Thread Tools Display Modes Linear Mode

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

 Contact - Home - Forums - Cryptocurrency Forum - Top