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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 B denote the matrix given below. (i) Find all eigenvalues of the matrix B. (ii) For each eigenvalue of B, find an associated eigenvector. (iii) Is the matrix B diagonalizable? Explain. (iv) Find all eigenvalues of the matrix 2B + 31, where I is the identity matrix. 41. 45. 49. 53. 57. 1 0 1 010 10 1 1 -3 0 0 1 000 3 1 01 0 0 1 1 02 000 201 030 102 42. 46. 50. 54. 10 030 101 101 020 101 000 102 020 02 20 -1 00 20 -1 0 2 58. 0 -1 0 43. 0 47. 51. 1 0 -1 1 0 1 55. 000 1 0 1 01 0 0 0 302 020 -1 0 1 02 0 10 -1 20-2 59. -1 1 2 10 -1 1 44. 0 1 48. 52. 56. 60. 0 -20 0 00 201 010 010 101 000 0 02 -1 0 2 -1 0 1 2 0 1 1 0
Transcribed Image Text:Problem III Let B denote the matrix given below. (i) Find all eigenvalues of the matrix B. (ii) For each eigenvalue of B, find an associated eigenvector. (iii) Is the matrix B diagonalizable? Explain. (iv) Find all eigenvalues of the matrix 2B + 31, where I is the identity matrix. 41. 45. 49. 53. 57. 1 0 1 010 10 1 1 -3 0 0 1 000 3 1 01 0 0 1 1 02 000 201 030 102 42. 46. 50. 54. 10 030 101 101 020 101 000 102 020 02 20 -1 00 20 -1 0 2 58. 0 -1 0 43. 0 47. 51. 1 0 -1 1 0 1 55. 000 1 0 1 01 0 0 0 302 020 -1 0 1 02 0 10 -1 20-2 59. -1 1 2 10 -1 1 44. 0 1 48. 52. 56. 60. 0 -20 0 00 201 010 010 101 000 0 02 -1 0 2 -1 0 1 2 0 1 1 0
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