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October 20th, 2013, 03:47 AM  #1 
Newbie Joined: Dec 2012 Posts: 22 Thanks: 0  Homogenous system with more variables than equations
Did I solve this correctly? Solve the system. 3u  v + w 5x  y = 0 6u  2v + 2w  9x + y = 0 9u + 3v  3w + 11x y = 0 Augmented matrix: My answer: u  1/3v + 1/3 w = 0 u = 1/3(v  w) where v and w are any real numbers. v = 3u + w, where u and w are any real numbers. w = v  3u, where v and u are any real numbers. I was told that I should set v and w to any arbitrary variable and then solve. Such as, let v = p and w = q, where p and q are any real numbers. I agree that this is one way to solve the system, but I don't see how my solution does not. Any suggestions? 
October 20th, 2013, 03:52 AM  #2 
Newbie Joined: Dec 2012 Posts: 22 Thanks: 0  Re: Homogenous system with more variables than equations
Edit: My answer also included x = 0 and y = 0.

October 20th, 2013, 02:57 PM  #3 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Homogenous system with more variables than equations
You are writing u , v , and w in terms of each other so it looks 'circular'. Since v and w are free variables the convention is to rename them , this will give v = p w = q u = 1/3(p  q) x = 0 y = 0 Now , make arbitrary choices for p and q to get u , v , w , x , y to avoid the circular reasoning. 
October 20th, 2013, 04:58 PM  #4 
Newbie Joined: Dec 2012 Posts: 22 Thanks: 0  Re: Homogenous system with more variables than equations
Thanks, that makes sense now. Guess I have to admit it: I was wrong.

October 22nd, 2013, 02:27 AM  #5  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Homogenous system with more variables than equations Quote:
 

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