# HW6 - COT 3502 Computer Model Formulation Spring 2008 1...

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COT 3502 Computer Model Formulation Spring 2008 1 Homework # 6 Due Thursday, March 20 All problems except #1 and #2 should be solved using VB. 1. (3 points) As we discussed in class, once you have performed the LU decomposition of a matrix, it is much less time consuming to solve the linear equations with the same left-hand side but different right-hand sides. Using the Gauss-Jordan method, obtain the matrices U and L - 1 of the LU decomposition of the matrix A = 1 2 0 1 1 1 1 2 1 . (1) Then, using the obtained matrices U and L - 1 , solve the equations A x = b with (a) b = 1 2 3 and (b) b = 2 0 - 1 . (2) 2. (3 points) Our proof of LU decomposition relied on the fact that the product of two lower triangular matrices is still a lower triangular matrix. Prove this fact! 3. (3 points) Consider the subroutine Gauss which you have developed for the previous homework. Modify this subroutine to perform pivoting before every step of the Gaussian elimination.

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