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Unformatted text preview: MthSc810 Mathematical Programming Fall 2011, solutions to Homework #7. Problem 1. Suppose three bases have the corresponding matrices B 1 , B 2 , B 3 : B 1 = 1 0 0 0 1 0 0 0 1 ; B 2 = 1 3 0 2 0 5 1 ; B 3 =  1 3 0 4 2 0 2 5 1 ; Compute square matrices E 2 , E 3 such that B k = B k 1 E k , with k { 2 , 3 } . Solution. Since B 2 = B 1 E 2 and B 1 = I , E 2 = B 2 . Because B 2 and B 3 only differ for the first column, E 3 = a 0 0 b 1 0 c 0 1 for some a, b, c that solve the following system of equations: 1 3 0 2 0 5 1 a b c =  1 4 2 . As described in the notes, solve first the equation with one nonzero coeffi cient, 2 b = 4 b = 2, then the other two: a + 3 2 = 1 a = 7 5 2 + c = 2 c = 12 Hence E 3 =  7 0 0 2 1 0 12 0 1 . Problem 2. Solve the KleeMinty example for n = 2 using the simplex method (feel free to use dictionaries or tableaux). Note that you should visit four bases.(feel free to use dictionaries or tableaux)....
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This note was uploaded on 03/14/2012 for the course MTHSC 810 taught by Professor Staff during the Fall '08 term at Clemson.
 Fall '08
 Staff
 Math, Matrices

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