# HW9 - Math 3013 Homework Set 9 Problems from 5.1(pgs...

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Math 3013 Homework Set 9 Problems from § 5.1 (pgs. 300-301 of text): 2,4,6,8,10,12,17,19,23 Problems from § 5.2 (pgs. 315-317 of text): 1,2,3,4,5,9,10,13 Problems from § 7.1 (pgs. 394-395 of text): 7,8,9,10 1. (Problems 5.1.2, 5.1.4, 5.1.6, 5.1.8, 5.1.10, and 5.1.12 in text). Find the characteristic polynomial, the real eigenvalues, and the corresponding eigenvectors for the following matrices. (a) A = ± 7 5 - 10 - 8 ² (b) A = ± - 7 - 5 16 17 ² (c) A = ± 1 - 2 1 2 ² (d) A = - 1 0 0 - 4 2 - 1 4 0 3 (e) A = 1 0 0 - 8 4 - 5 8 0 9 (f) A = - 4 0 0 - 7 2 - 1 7 0 3 2. (Problems 5.1.17 and 5.1.19 in text) Find the eigenvalues λ i and the corresponding eigenvectors v i for the following linear transformations. (a) T ([ x, y ]) = [2 x - 3 y, - 3 x + 2 y ] (b) T ([ x 1 , x 2 , x 3 ]) = [ x 1 + x 3 , x 2 , x 1 + x 3 ] 3. Mark each of the following statements True or False . (a) Every square matrix has real eigenvalues. (b) Every

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## This homework help was uploaded on 04/22/2008 for the course MATH 3613 taught by Professor Binegar during the Spring '08 term at Oklahoma State.

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HW9 - Math 3013 Homework Set 9 Problems from 5.1(pgs...

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