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# HW1 - MAE 107 Computational Methods Summer Session II 2009...

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MAE 107 – Computational Methods Summer Session II 2009 Homework # 1 due on Wednesday, August 12 in class 4 problems – 20 points Guidelines : Please turn in a neat homework that gives all the formulae that you have used and all the necessary information for the grader to understand your solution. Also, if the problem requires you to write a MATLAB code, please turn in, along with the written explanation of your solution, (i) a copy of the code you used, carefully documented with comments and using proper indentation, and (ii) the requested ouputs and graphs. Problem 1 – 4 points 1. Compute manually the eigenvalues of the matrix A = 0 - 1 - 1 - 2 1 - 2 1 - 1 2 . (Remember that λ is an eigenvalue of A if | A - λ I | = 0 with I the identity matrix – Hint: one of the eigenvalue is equal to 1). For each of the eigenvalues compute an associated eigenvector. 2. In MATLAB, write a short script file that defines the matrix A as a 3 × 3 array and computes the eigenvalues and eigenvectors of A using the eig function of MATLAB. Compare with your response to the previous question (remember that if x is an eigenvector, then α x

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