IEOR162_hw01 - IEOR 162, Spring 2012 Homework 01 1....

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Unformatted text preview: IEOR 162, Spring 2012 Homework 01 1. (Modified from Problem 2.3.6; 10 points) Consider a linear system 2 x 2 + 2 x 3 = 4 x 1 + 2 x 2 + x 3 = 4 x 2- x 3 = 0 . Use Gauss-Jordan elimination to determine whether the system has a unique solution, infinitely many solutions, or no solution. In the first two cases, write down the solution(s) explicitly. 2. (Modified from Problem 2.3.8; 10 points) Consider a linear system x 1 + x 2 + x 3 = 1 x 2 + 2 x 3 + x 4 = 2 x 4 = 3 . Use Gauss-Jordan elimination to determine whether the system has a unique solution, infinitely many solutions, or no solution. In the first two cases, write down the solution(s) explicitly. 3. (Modified from Problem 2.5.2; 10 points) Use Gauss-Jordan elimination to find the inverse of the matrix 1 0 1 4 1- 2 3 1- 1 . 4. (Modified from Problem 3.2.3; 10 points) Leary Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B, and 1 of C. Running process 2 for an hour costs $1 andhour costs $4 and yields 3 units of A, 1 of B, and 1 of C....
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