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before programming an algorithm which implements the simplex method, I thought I'd solve an issue before the actual programming work begins.

For some reason, I can NEVER get the correct answer. I've understood the method, but the problem is with the row operations - where you try to get a column to have all 0 values except for the pivot element which has a value of '1'.

To do this, I play around with the rows by doing R1-R2, R2+5R1, etc. I always manage to get the pivot column to be 1 and the rest 0's, however my answers never match the correct ones. Ive narrowed it down to a problem with the row operations - are there any rules related to this, or can I just play around with the rows as much as I like? Also, can I mix between older tableaux and the current one?

Thanks

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    If you want, feel free to post a sample table and I'll be more specific about what went wrong. Let me know if you want to know a "always do this row operation" rule. I assume you've learned them, and are just curious why being creative messes things up.2011-05-16
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    Unfortunately I haven't come across any specific row operation rules - which is why I'm searching for guidelines :) What I usually do is play around with a mixture of rows from the same table and previous tables, and add/subtract them to get the required column completely with 0's except for the pivot - which works, however answers never match the supposed correct ones. Therefore, I'm definitely doing something wrong with the row operations.2011-05-16
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    Cool. I think you'll get it if you remember the rule: The first row you mention is the one you want to change. The second row you mention has to be the new pivot row. Choose the multiplier so it cancels. If both rows are the same (you are trying to fix the pivot row), the only thing you do is divide the pivot row by whatever number is in the pivot position, so you get a 1.2011-05-16
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    In linear systems you have more flexibility, especially at the start. Row swaps, random row ops, etc. can make a problem easier. Towards the end of it (after REF and on the way to RREF), things get more tightly controlled. The simplex algorithm is the most restrictive because you are already in RREF, and one wrong move can break the RREF pivots.2011-05-16
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    Ah I see. So for example to change R1 and the pivot row is R2, I would use R1+5R2. And for R3, I'd use R3-4R2? And if I use this system, would it be guaranteed to work all the time? Thanks for all the help so far :)2011-05-16
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    Yup. This is guaranteed to keep the matrix in RREF. —— You have to choose pivots correctly to keep the other 3 • happy. To make progress on #3, choose pivot columns with negative bottom entries. To keep #2, choose the pivot row correctly using the ratio. To keep #4, never choose the last row as the pivot row.2011-05-16
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    Thanks so much! This information really helped me :)2011-05-16

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