assign4.sol

# assign4.sol - ASE 211 Homework 4 1. Solve (by hand) Ax = b...

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ASE 211 Homework 4 1. Solve (by hand) A x = b where A = 4 - 1 2 - 7 - 5 - 4 5 / 2 2 - 13 / 2 and b = 1 2 3 Using Gauss. Elim Method. P = 1 0 0 0 1 0 0 0 1 The Augmented Matrix. 4 - 1 2 | 1 - 7 - 5 - 4 | 2 5 / 2 2 - 13 / 2 | 3 | - 7 | > | 4 | > | 2 . 5 | hence pivot. P = 0 1 0 1 0 0 0 0 1 - 7 - 5 - 4 | 2 4 - 1 2 | 1 5 / 2 2 - 13 / 2 | 3 Multiply row 1 by -4/7 and subtract from row 2. Muliply row 1 by -5/14 and subtract from row 3. - 7 - 5 - 4 | 2 0 - 27 / 7 - 2 / 7 | 15 / 7 0 3 / 14 - 111 / 14 | 52 / 14

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No Pivot required. Multiplying row 2 by 7 and row 3 by 14 we get. - 7 - 5 - 4 | 2 0 - 27 - 2 | 15 0 3 - 111 | 52 Multiplying row 3 by -9 and subtracting row 2 from row 3 we get, - 7 - 5 - 4 | 2 0 - 27 - 2 | 15 0 0 - 1001 | 483 Hence, after backward substitution, x = [0 . 3613; - 0 . 5198; - 0 . 4825] 2. Compute (by hand) the LU factorization of the following matrix:
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## This note was uploaded on 03/20/2008 for the course ASE 211 taught by Professor N/a during the Spring '08 term at University of Texas.

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assign4.sol - ASE 211 Homework 4 1. Solve (by hand) Ax = b...

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