128ahw13sum10 - MATH 128A SUMMER 2010 HOMEWORK 13 SOLUTION...

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MATH 128A, SUMMER 2010, HOMEWORK 13 SOLUTION BENJAMIN JOHNSON Homework 13: Due Monday, August 9 6.5; 5a, 9a 6.6; 1ab 7.1; 1b, 4a section 6.5 5. Factor the following matrices into the LU decomposition using the LU Factorization Algo- rithm with l ii = 1 for all i . a. 2 - 1 1 3 3 9 3 3 5 Solution: Using Gaussian Elimination, we get 2 - 1 1 3 3 9 3 3 5 -→ R 2 - 1 . 5 R 1 R 2 R 3 - 1 . 5 R 1 R 3 2 - 1 1 0 4 . 5 7 . 5 0 4 . 5 3 . 5 -→ R 3 - R 1 R 3 2 - 1 1 0 4 . 5 7 . 5 0 0 - 4 So L = 1 0 0 1 . 5 1 0 1 . 5 1 1 and U = 2 - 1 1 0 4 . 5 7 . 5 0 0 - 4 . 9. Obtain factorizations of the form A = P t LU for the following matrices. a. A = 0 2 3 1 1 - 1 0 - 1 1 Solution: Using Gaussian Elimination, we get: 0 2 3 1 1 - 1 0 - 1 1 -→ R 1 R 2 1 1 - 1 0 2 3 0 - 1 1 -→ R 3 + 0 . 5 R 2 R 3 1 1 - 1 0 2 3 0 0 2 . 5 So P = 0 1 0 1 0 0 0 0 1 , and L
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128ahw13sum10 - MATH 128A SUMMER 2010 HOMEWORK 13 SOLUTION...

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