hw5 - Homework 5 Math 471 Fall 2007 Assigned Friday October...

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Homework 5 Math 471, Fall 2007 Assigned: Friday, October 5, 2006 Due: Friday, October 12, 2006 Include a cover page Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Pivoting) (a) Prove that the matrix 0 1 1 1 does not have an LU factorization. (b) Does the system 0 1 1 1 x y = a b have a unique solution for all a, b R ? Why? (c) How can you modify the matrix in part (a) so that it has an LU factorization? (2) (Gaussian Elimination with Partial Pivoting, p. 169, #7(a) BY HAND) Solve the following system using Gaussian elimination with partial pivoting. Show all intermediate matrices and the row vector at each step: 2 x 1 + 3 x 2 + x 3 = - 4 4 x 1 + x 2 + 4 x 3 = 9 3 x 1 + 4 x 2 + 6 x 3 = 0 (3) (Implementing PLU Factorization) Write a program to find the LU factorization of a given n × n matrix A using partial pivoting . Your Matlab file should be named myLU.m , and the first few lines should read
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