April 13th, 2010, 04:14 AM  #1 
Senior Member Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0  Simplification
Hi, I have the (*) x_1 + 3x_2 + 3x_3 + 2x_4 = 1 2x_1 + 6x_2 + 9x_3 + 5x_4 = 1 x_1 3x_2 + 3x_3 = k I have solved this using Gaussian Elimination down to the simplification of: x_1 + 3x_2 + 3x_3 + 2x_4 = 1 (i) 3x_2 + x_4 = 1 (ii) (x_2, x_4) are free variables denoted: A and B respectively. (ii) is simplified to; x_3 = ((1  B) / 3) Now, I'm having some trouble simplifying (i) I have gone, x_1 + 3A +3((1  B) / 3) + 2B = 1 x_1 = 1  3A  1  B  2B = 2  3A  B + 2B How can I simplify this further ? Thanks! wulfgarpro. 
April 13th, 2010, 10:20 AM  #2  
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0  Quote:
 
April 13th, 2010, 06:13 PM  #3 
Senior Member Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0  Re: Simplification
Well, If k = 3 there are infinite possible solutions; namely, x_1 + 3x_2 + 3x_3 + 2x_4 = 1 (i) 3x_2 + x_4 = 1 (ii) 0  0 + 0 = 0 (iii) This is because in row echelon form, k is k+3. If k != 3 there are no solutions because the system is inconsistent. So I just dropped it in this case; I'm trying to solve the system when k = 3. wulfgarpro. 
April 13th, 2010, 07:31 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,835 Thanks: 2162 
You get x_3 = (1  B)/3 and x_1 = 2  3A  B. Since A and B can have any values, you can't simply further.

April 13th, 2010, 10:49 PM  #5 
Senior Member Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0  Re: Simplification
Hm, I get x_1 = 3A  B If possible, could you show me how you got your solution in a stepwise fashion ? wulfgarpro. 
April 14th, 2010, 01:13 AM  #6 
Senior Member Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0  Re: Simplification
I got it: x_1 + 3A + 3((1  B) / 3) + 2B = 1 x_1 + 3A 1  B + 2B = 1 x_1 + 3A  B + 2B = 2 2  3A  B = x_1 wulfgarpro. 

Tags 
simplification 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Simplification  Chikis  Elementary Math  2  September 11th, 2013 10:11 AM 
simplification  arron1990  Algebra  3  August 14th, 2012 04:50 AM 
Need some help with simplification  p3aul  Algebra  5  January 23rd, 2011 09:11 PM 
Simplification  wulfgarpro  Algebra  7  April 18th, 2010 03:16 AM 
Simplification help  Salient  Algebra  3  October 21st, 2008 01:17 PM 