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 1 002 04(:D) 2 (1:5) + (1) 4(:)41.1 0042.10043. 2001000 100200100 145. 00101 053.57.46.0 1 11011 100400101000102049... (1) 50 (1) 44(:¦:-) (9)00351. 20-152.40120001 00 1054.-147. 0 020 2032 223222355.48.1 1 00 10 1 101 00040 1 056.1 11 -2 1-2 101 00 1 001 00 50(D)(-+) (9) - (-)1 1 158. 1 -1 159. 5 1 160. 1 -1 10 1 00 1001 00 10

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Answered: Problem III Let A denote the matrix…

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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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

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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