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Problem III Let A denote the matrix given below. (i) Find all eigenvalues of the matrix A. (ii) For each eigenvalue of A, find an associated eigenvector. (iii) Find a diagonal matrix D and an invertible matrix U such that A = UDU-¹. 41. 0 1 0 100 0 10 42. 0 1 0 100 020 0 2 0 43. 200 0 1 0 44. 0 4 0 100 0 1 0

Problem III Let A denote the matrix given below. (i) Find all eigenvalues of the matrix A. (ii) For each eigenvalue of A, find an associated eigenvector. (iii) Find a diagonal matrix D and an invertible matrix U such that A = UDU-¹. 41. 0 1 0 100 0 10 42. 0 1 0 100 020 0 2 0 43. 200 0 1 0 44. 0 4 0 100 0 1 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Please solve parts 41-44 of this problem... take as much time as necessary... this is for Linear algebra review

Problem III Let A denote the matrix given below. (i) Find all eigenvalues of the matrix A. (ii) For each eigenvalue of A, find an associated eigenvector. (iii) Find a diagonal matrix D and an invertible matrix U such that A = UDU-¹. 0 1 0 0 2 0 4(:D) 2 (1:5) + (1) 4(:) 41. 1 00 42. 100 43. 200 100 0 10 020 010 0 1 45. 001 01 0 53. 57. 46. 0 1 1 101 1 10 04 001 010 0 01 020 49. .. (1) 50 (1) 44(:¦:-) (9) 0 03 51. 20-1 52. 401 20 0 01 0 0 1 0 54. -1 47. 0 02 0 20 32 2 232 223 55. 48. 1 1 0 0 1 0 1 1 01 0 004 0 1 0 56. 1 1 1 -2 1 -2 1 01 0 0 1 0 01 0 0 50 (D)(-+) (9) - (-) 1 1 1 58. 1 -1 1 59. 5 1 1 60. 1 -1 1 0 1 0 0 10 01 0 0 10
Transcribed Image Text:Problem III Let A denote the matrix given below. (i) Find all eigenvalues of the matrix A. (ii) For each eigenvalue of A, find an associated eigenvector. (iii) Find a diagonal matrix D and an invertible matrix U such that A = UDU-¹. 0 1 0 0 2 0 4(:D) 2 (1:5) + (1) 4(:) 41. 1 00 42. 100 43. 200 100 0 10 020 010 0 1 45. 001 01 0 53. 57. 46. 0 1 1 101 1 10 04 001 010 0 01 020 49. .. (1) 50 (1) 44(:¦:-) (9) 0 03 51. 20-1 52. 401 20 0 01 0 0 1 0 54. -1 47. 0 02 0 20 32 2 232 223 55. 48. 1 1 0 0 1 0 1 1 01 0 004 0 1 0 56. 1 1 1 -2 1 -2 1 01 0 0 1 0 01 0 0 50 (D)(-+) (9) - (-) 1 1 1 58. 1 -1 1 59. 5 1 1 60. 1 -1 1 0 1 0 0 10 01 0 0 10
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