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 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
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 Originally Posted by wulfgarpro 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)
What happened to the "k" in the third (original) equation? 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 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 Chikis Elementary Math 2 September 11th, 2013 10:11 AM arron1990 Algebra 3 August 14th, 2012 04:50 AM p3aul Algebra 5 January 23rd, 2011 09:11 PM wulfgarpro Algebra 7 April 18th, 2010 03:16 AM Salient Algebra 3 October 21st, 2008 01:17 PM

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