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Compute the eigenvalues and associated eigenvectors of the following matrices. 4 0 0 2

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 2 Chapter 7.2

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 2

Compute the eigenvalues and associated eigenvectors of the following matrices. 4 0 0 2 -1 a. d. 1 -2 1 -2 b. -1 i 3 -1 i 6 3 2 --1 1 2 0 0 I -2 3 e. -1 1 2 0 2 0 4 2 2 _ i 3 J C. f

Step-by-Step Solution:
Step 1 of 3

3/2/2016 Trigonometric Substitutions (Sect. 7.2) Things to know: sin(x)+cos2(x=1∧1+tan 2(x=sec 2(x)  This allows you to compute the integrals containing the following expressions. b −x usesin (u) x +b usetan (u)  √ √ 2 2 1  √ x −b usesec(u)∨ cos(u) ≠  b is any real number 0 b −x dx  ∫ √  Substitute bsin(u) for the value of x  x = bsin(u)  dx = bcos(u)du  ∫ √b −b sin (u) bcos(u)du  Factor out the b2 1−sin (u) ¿ b ¿  √ ¿ ∫ ¿ 2 2 2

Step 2 of 3

Chapter 7.2, Problem 2 is Solved
Step 3 of 3

Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Compute the eigenvalues and associated eigenvectors of the following matrices. 4 0 0 2