quiz1solutions

quiz1solutions - 640:354:01, 01/29/07 Quiz #1, with...

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640:354:01, 01/29/07 Quiz #1, with solutions 1. What is the rank of the following matrix? (Justify!) A = 0 1 2 3 1 2 3 4 1 1 1 1 Solution: The reduced row echelon form of A is A = 1 0 - 1 - 2 0 1 2 3 0 0 0 0 . The rank of the matrix is equal to the number of nonzero rows in its reduced row echelon form. Therefore, the rank of A is 2. 2. Write an equivalent LP in standard form: Minimize z = 2 x 1 + 3 x 2 - x 3 , subject to x 1 - 10 x 2 + x 3 4 x 1 + x 3 = 2 x 1 0 ,x 2 0 Solution: LP in standard form is “Maximize c T x subject to Ax b,x 0 .” There are three things to be done: 1. Convert minimization into maximization: Minimize z = 2 x 1 + 3 x 2 - x 3 becomes Maximize - 2 x 1 - 3 x 2 + x 3 2. Make all inequalities and equations (except non-negativity constraints) into inequalities
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quiz1solutions - 640:354:01, 01/29/07 Quiz #1, with...

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