An n x n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. Find the characteristic polynomial, eigenvalues, and eigenvectors of each of the following matrices, if there exist. (1) (4) [39]. 0 1] 0 1 0 1 0 1 1 0 1 0 1 0 1 0 " 1 2 3] 2 3 0 3 (2) 0 (5) - P 77 T L T 2 T (3) (6) [-2 0 0] 3 23 4 -1 6 0500 00 " 0 -5 0 0ela nad DONO' 02 00-2 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please let me know number (4),(6)

6.1. An n x n matrix A is diagonalizable if and only if A has n linearly independent
eigenvectors. Find the characteristic polynomial, eigenvalues, and eigenvectors of
each of the following matrices, if there exist.
(1)
(4)
3
9
0 1 0
101 0
0101
1 0 1 0
12
9
1 2 3
(2) 0 2 3
0
0
3
(5)
1
1
1
1
9
1
1
1
1
1
1
1
1 1
1 1 1
9
(3)
(6)
[-2
00
3
2 3
4 -1 6
0-5 0
5 00
00
0 2
500
9
07sala nadT
0
-2
0
Transcribed Image Text:6.1. An n x n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. Find the characteristic polynomial, eigenvalues, and eigenvectors of each of the following matrices, if there exist. (1) (4) 3 9 0 1 0 101 0 0101 1 0 1 0 12 9 1 2 3 (2) 0 2 3 0 0 3 (5) 1 1 1 1 9 1 1 1 1 1 1 1 1 1 1 1 1 9 (3) (6) [-2 00 3 2 3 4 -1 6 0-5 0 5 00 00 0 2 500 9 07sala nadT 0 -2 0
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