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HW7 - z z = re iθ obtain z 3 √ z 1/z 2 and ¯ z 4 Obtain...

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COT 3502 Computer Model Formulation Spring 2008 1 Homework # 7 Due Tuesday, April 8 Problems in this homework do not require coding. 1. Obtain the norms || · || 1 and || · || of the following vector and matrix: v = 1 3 1 , A = 2 3 1 6 8 . 999 2 - 4 - 5 . 999 0 . (1) 2. Compute the condition number for the matrix A considered in the pre- vious problem. Use the norm || · || 1 in this calculation. You may use your Gaussian elimination code to obtain A - 1 (instead of computing it by hand). Based on your result, would you call a system of equations A x = b with this matrix A well- or ill-defined? 3. Using the polar coordinate representation of a complex number
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Unformatted text preview: z , z = re iθ , obtain: z 3 , √ z , 1 /z 2 , and ¯ z 4. Obtain all values of 4 √-2 i , i.e. all complex numbers z such that z 4 =-2 i . 5. Consider the following system of ordinary differential equations (ODEs): d x dt = A x , A = ± 2-1 3 ! . (2) (a) Obtain the eigenvalues and the eigenvectors of the matrix A . (b) Obtain the general solution of this equation. (c) Obtain the solution that corresponds to the initial conditions x (0) = (1 ,-1), 6. Solve problem 5 for the following system of ODEs: d x dt = A x , A = ± 1-2 2 1 ! . (3)...
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