# hw8 - Assignment#8 Solving Systems of Linear Equations...

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Assignment #8: Solving Systems of Linear Equations using Naïve Gaussian Elimination Due date: Wednesday, November 10, 2010 (10:10am) For full credit you must show all of your work. 1. In plain English and in your own words, describe the main steps in the naïve Gaussian elimination algorithm and discuss its principal weaknesses. 2. Show what happens when you try to solve each of the following systems, by hand, using the naïve Gaussian elimination algorithm. You will find that the method fails, for different reasons, in each case. Explain the failures, and, for each system, determine the solution by other means. a. 3 x + 2 y = " 10 " x " 2 3 y = 5 b. 30 x " 15 y = 120 " 2 x + y = " 8 c. x 1 + x 2 + 2 x 3 = 3 x 1 + x 2 + 4 x 3 = 5 2 x 1 + x 2 + 3 x 3 = 6 3. Solve the following system by hand using naïve Gaussian elimination. In this case, the method will not fail. For full credit, you must show all of the steps in your work. 2

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hw8 - Assignment#8 Solving Systems of Linear Equations...

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