
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 v1v2, v2v3 and v3v1 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: 6,510 Thanks: 584 
(i) Assume a(v1v2)+b(v2v3)+c(v3v1)=0. Then (ac)v1+(ba)v2+(cb)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. 

Tags 
dependence, independence, linear 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Determine linear dependence over Z2  phongchaychua  Linear Algebra  2  April 27th, 2014 05:08 AM 
Linear independence  limes5  Linear Algebra  4  February 22nd, 2013 10:22 PM 
Linear Dependence Equation  Spennet  Linear Algebra  2  August 18th, 2011 08:00 AM 
Linear Dependence Proof  Singularity  Linear Algebra  1  February 4th, 2010 05:32 PM 
Linear independence of {1,x,...,x^n}  isaace  Linear Algebra  2  November 29th, 2008 11:06 PM 