iagonalize the following matrix: 21 4 1-4 31 -1 24001₁ 111-12 C - 0

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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Question
Diagonalize the following matrix:
2
4
3
1
0
−1 4
1 - 1
40 0
0 2 0
00
=
400
400
1 1 1
020 = 0 0 1
001
0 1 1
1 1 1
1 -1 0
20 1
0
0 0 -2
10 =
not diagonalization
1 - 1 1
1 1 0
01 1
2 10
4-1 -4
3 1
- 1
2 1
4
3
1
0
-4
1 - 1
2 1
4
3
1 −1 1
-
001
1
0
0
1 - 4
1 - 1
1 1 1
1 -1 0
20 1
1
1 -1 1
1
10
0
1 1
Transcribed Image Text:Diagonalize the following matrix: 2 4 3 1 0 −1 4 1 - 1 40 0 0 2 0 00 = 400 400 1 1 1 020 = 0 0 1 001 0 1 1 1 1 1 1 -1 0 20 1 0 0 0 -2 10 = not diagonalization 1 - 1 1 1 1 0 01 1 2 10 4-1 -4 3 1 - 1 2 1 4 3 1 0 -4 1 - 1 2 1 4 3 1 −1 1 - 001 1 0 0 1 - 4 1 - 1 1 1 1 1 -1 0 20 1 1 1 -1 1 1 10 0 1 1
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