hw1 - 3. If       = 2 01 . 1 2 1 A , find...

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ME 4905 2008 Advanced Numerical Methods for Engineers Homework 1 (Due date: 16 Sept in the class) 1. If the determinant of the coefficient matrix A is zero, what can you say about the system? 2. Consider the following linear system: 11 4 2 3 2 5 2 8 4 = + + = + + = + - z y x z y x z y x a) Find the determinant of the coefficient matrix. b) Solve the system by hand calculation. c) Solve the system using the Matlab code (Gauss-Seidel method) provided in the lecture notes. d) Solve the system using Matlab built-in function.
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Unformatted text preview: 3. If       = 2 01 . 1 2 1 A , find the condition number of A based on the uniform matrix norm. Check your answer by comparing your results to the results generated by Matlab program. Is this a well-conditioned matrix? 4. Given ∑ = ≤ ≤ ∞ = n j ij n i a A 1 1 max , prove that ∞ ∞ ∞ + ≤ + B A B A . (Hint: use the fact that b a b a + ≤ + if a and b are real numbers.)...
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This note was uploaded on 01/17/2010 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.

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