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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. 0 1 0 1 0 41. ¹ (¦ D) (: :) 42. 1 0 0 020 010 0 0 001 01 0 45. 02 49. 1 0 1 020 46. 50. 4 001 01 0 10 103 010 0 2 0 43. 200 010 47. 0 -1 0 0 02 0 20 01 51. 2 0-1 01 0 44. 48. 0 4 100 010 01 0 004 010 0 2 0 52. 4 0 1 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. 0 1 0 1 0 41. ¹ (¦ D) (: :) 42. 1 0 0 020 010 0 0 001 01 0 45. 02 49. 1 0 1 020 46. 50. 4 001 01 0 10 103 010 0 2 0 43. 200 010 47. 0 -1 0 0 02 0 20 01 51. 2 0-1 01 0 44. 48. 0 4 100 010 01 0 004 010 0 2 0 52. 4 0 1 0 1 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. 0 1 0 1 0 2 0 4 41. -(:D) - (:D) * () +(:) 1 00 42. 100 43. 200 100 0 10 020 0 1 45. 0 0 1 01 0 53. 57. 46. 0 1 1 10 1 1 10 04 001 010 0 01 020 49. .. (1) 50 (1) 4(:¦:-) (9) 0 103 51. 2 0 -1 52. 401 2 01 0 010, -1 47. 0 02 20 0 32 2 54. 232 223 55. 48. 110 0 1 0 1 1 010 004 0 1 0 56. 1 1 1 -2 1 -2 1 01 0 0 1 0 01 0 0 50 (D)(-+) (9) -(-5) 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 1 0 2 0 4 41. -(:D) - (:D) * () +(:) 1 00 42. 100 43. 200 100 0 10 020 0 1 45. 0 0 1 01 0 53. 57. 46. 0 1 1 10 1 1 10 04 001 010 0 01 020 49. .. (1) 50 (1) 4(:¦:-) (9) 0 103 51. 2 0 -1 52. 401 2 01 0 010, -1 47. 0 02 20 0 32 2 54. 232 223 55. 48. 110 0 1 0 1 1 010 004 0 1 0 56. 1 1 1 -2 1 -2 1 01 0 0 1 0 01 0 0 50 (D)(-+) (9) -(-5) 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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