Homework 1 Solution - MAT 242 Written Homework#1 EP1.2/H1.1...

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MAT 242 Written Homework #1 SOLUTIONS EP1.2/H1.1 Due: January 23/24 Solve the following problems, showing any necessary work. This includes row operations. 1. Use Gaussian Elimination (with matrices and row operations) and back-substitution to solve the fol- lowing system of linear equations. 2 x + 3 y - 5 z = 9 2 x + y - 4 z = - 26 x + y - 2 z = - 1 Solution: Typical row operations are shown below. 2 3 - 5 2 1 - 4 1 1 - 2 9 - 26 - 1 ------→ 1 - 3 1 2 - 3 2 1 - 4 1 1 - 2 10 - 26 - 1 -------→ 2 - 2 1 1 2 - 3 0 - 3 2 1 1 - 2 10 - 46 - 1 ------→ 3 - 1 1 2 - 3 0 - 3 2 0 - 1 1 10 - 46 - 11 -------→ 2 - 4 3 1 2 - 3 0 1 - 2 0 - 1 1 10 - 2 - 11
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