IEOR162_hw01

# IEOR162_hw01 - IEOR 162 Spring 2010 Suggested Solution to...

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IEOR 162, Spring 2010 Suggested Solution to Homework 01 Problem 2.3.7 First we represent this linear system in the augmented matrix form 1 1 0 2 0 - 1 2 3 0 1 1 3 . Then we apply the Gauss-Jordan elimination as follows: 1 1 0 2 0 - 1 2 3 0 1 1 3 1 1 0 2 0 1 - 2 - 3 0 1 1 3 1 0 2 5 0 1 - 2 - 3 0 0 3 6 1 0 2 5 0 1 - 2 - 3 0 0 1 2 1 0 0 1 0 1 0 1 0 0 1 2 . With this we know the solution is x 1 = 1, x 2 = 1, and x 3 = 2. Problem 2.3.8 First we represent this linear system in the augmented matrix form 1 1 1 0 1 0 1 2 1 2 0 0 0 1 3 . Then we apply the Gauss-Jordan elimination as follows: 1 1 1 0 1 0 1 2 1 2 0 0 0 1 3 1 0 - 1 - 1 - 1 0 1 2 1 2 0 0 0 1 3 1 0 - 1 0 2 0 1 2 0 - 1 0 0 0 1 3 . With this we know there are infinitely many solutions. If we choose x 3 = k , the set of solutions can be represented as x 1 = 2 + k x 2 = - 1 - 2 k x 3 = k x 4 = 3 .

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