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 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded 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

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