Question #3*: Let the matrices A₁, A₂ and A3 be such that: 2 3 4-4-4-4-[9] A₂ = -1 5 A₁ 2 -1 3 -2 A3 = 0 6 -5 a) Find the eigenvalues and the eigenvectors of A₁, A₂ and A. b) Diagonalize the matrices A₁, A₂and A. c) Compute A₁, A₂, A₂k, e¹¹, ¹2 and ¹3. k k ,е d) Let v= [35], compute 4,2000,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question #3*: Let the matrices A₁, A, and A3 be such that:
2
A₁ =
2 −1
3
-2
9
A₂
=
9
2 3
5
9
A3
A3
=
a) Find the eigenvalues and the eigenvectors of A₁, A₂ and A3.
2
0 6
-1 -5
b) Diagonalize the matrices A₁, A₂and A.
k
c) Compute A₁ A₂, A₂, e¹
2
d) Let v=[35]", compute 4,2000,
et, et andet.
Transcribed Image Text:Question #3*: Let the matrices A₁, A, and A3 be such that: 2 A₁ = 2 −1 3 -2 9 A₂ = 9 2 3 5 9 A3 A3 = a) Find the eigenvalues and the eigenvectors of A₁, A₂ and A3. 2 0 6 -1 -5 b) Diagonalize the matrices A₁, A₂and A. k c) Compute A₁ A₂, A₂, e¹ 2 d) Let v=[35]", compute 4,2000, et, et andet.
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