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Problem 5 Consider the matrix A = (a) Find the eigenvalues of A. (A₁ A₁ = A₂ = A3 = cont. A. O(A)T₁= (b) Find the corresponding normalized eigenvectors of O(B)₁ = 0 0 (:) 0 (E)= , *₂ = 0(D)₁=2 0 ₂= 1 2 0 2 0-2 0 2 0 -1 (2 0 1 #₂ 1 0 O(C)1=0,2 = √2 = A₂ ≤ √3) -2 √5 #3 = 0 1 1 0 (.). -- () -- () = 0 1 = 1 0 2 0 30 - - () 1 = -23/3 1

Problem 5 Consider the matrix A = (a) Find the eigenvalues of A. (A₁ A₁ = A₂ = A3 = cont. A. O(A)T₁= (b) Find the corresponding normalized eigenvectors of O(B)₁ = 0 0 (:) 0 (E)= , *₂ = 0(D)₁=2 0 ₂= 1 2 0 2 0-2 0 2 0 -1 (2 0 1 #₂ 1 0 O(C)1=0,2 = √2 = A₂ ≤ √3) -2 √5 #3 = 0 1 1 0 (.). -- () -- () = 0 1 = 1 0 2 0 30 - - () 1 = -23/3 1

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 5 2 0 2 0 -1 (a) Find the eigenvalues of A. (A₁ A₂ ≤ A3) Consider the matrix A = λι = A₂ = A3 = cont. A. (b) Find the corresponding normalized eigenvectors of O(A)*₁ = O(B)₁ = 0 (E)= 0 (:) 0 1,₂0 23/0 2 0 0-2 0(D)₁=2 0 ₂= 1 #3 = (2 0 O(C)1=0,2 = √2 1 0 1 #₂ -2 = 1 1 0 (.). -- () -- () = 0 = 1 1 0 2 0 √5 13 = √3 () -2,3= 1 1
Transcribed Image Text:Problem 5 2 0 2 0 -1 (a) Find the eigenvalues of A. (A₁ A₂ ≤ A3) Consider the matrix A = λι = A₂ = A3 = cont. A. (b) Find the corresponding normalized eigenvectors of O(A)*₁ = O(B)₁ = 0 (E)= 0 (:) 0 1,₂0 23/0 2 0 0-2 0(D)₁=2 0 ₂= 1 #3 = (2 0 O(C)1=0,2 = √2 1 0 1 #₂ -2 = 1 1 0 (.). -- () -- () = 0 = 1 1 0 2 0 √5 13 = √3 () -2,3= 1 1
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