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 Linear Algebra Linear Algebra Math Forum

 March 28th, 2015, 10:30 PM #1 Newbie   Joined: Mar 2015 From: Singapore Posts: 1 Thanks: 0 Linear independence & linear dependence Suppose that vectors v1,v2,v3 are linearly independent. (i) Prove that v1-v2, v2-v3 and v3-v1 are linearly dependent. (ii) Prove that v1+v2, v2+v3 and v3+v1 are linearly dependent. I need you guys to help me solve this question because I'm stucked in this question for few hours already thanks in advance! March 29th, 2015, 02:14 PM #2 Global Moderator   Joined: May 2007 Posts: 6,703 Thanks: 669 (i) Assume a(v1-v2)+b(v2-v3)+c(v3-v1)=0. Then (a-c)v1+(b-a)v2+(c-b)v3=0. Linear independence forces a=b=c, so the difference vectors are dependent, using the same coefficient for each. (ii)When you work with the sum vectors, you end up with a=-c, b=-a, c=-b, which forces a=b=c=0, so the sum vectors are independent. Thanks from Country Boy Tags dependence, independence, linear 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 phongchaychua Linear Algebra 2 April 27th, 2014 05:08 AM limes5 Linear Algebra 4 February 22nd, 2013 10:22 PM Spennet Linear Algebra 2 August 18th, 2011 08:00 AM Singularity Linear Algebra 1 February 4th, 2010 05:32 PM isaace Linear Algebra 2 November 29th, 2008 11:06 PM

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