A. C. D. A = -3 5 -1 a22 3] -3 0 a33- X1 - 19. λ₁ = -2, X₂ = 1 X3 8 ;) Find the values of a11, a22, and a23 such that x₁ is an eigenvector of matrix A and 2₁ is the corresponding eigenvalues. ) Given the other 2 eigenvectors, X₁ and x2, find the remaining two eigenvalues, A₁ and 2₂, of A. ) Based on your answers from part A and part B, state why matrix A is diagonalizable. Write down the matrix of eigenvectors X= [X₁, X2, X3] and the diagonalization matrix A.
A. C. D. A = -3 5 -1 a22 3] -3 0 a33- X1 - 19. λ₁ = -2, X₂ = 1 X3 8 ;) Find the values of a11, a22, and a23 such that x₁ is an eigenvector of matrix A and 2₁ is the corresponding eigenvalues. ) Given the other 2 eigenvectors, X₁ and x2, find the remaining two eigenvalues, A₁ and 2₂, of A. ) Based on your answers from part A and part B, state why matrix A is diagonalizable. Write down the matrix of eigenvectors X= [X₁, X2, X3] and the diagonalization matrix A.
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
Please Help!!!!!
![Given the following,
B.
A = -1
C.
D.
-3
922
0
5
3
a33
X1 =
1
λ₁ = -2,
X2 =
1
A. (-) Find the values of a11, a22, and a23 such that X₁ is an eigenvector of matrix A and 2₁ is
the corresponding eigenvalues.
) Given the other 2 eigenvectors, X₁ and X2, find the remaining two eigenvalues, λ₁ and ₂,
of A.
X3 = 8
[3]
) Based on your answers from part A and part B, state why matrix A is diagonalizable.
Write down the matrix of eigenvectors X = [X₁, X2, X3] and the diagonalization matrix A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F547803a6-40ba-407b-9edd-fe79ffc19960%2F20c0e909-ac6f-4229-aae5-3e4dad4dde93%2Fdycd70k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the following,
B.
A = -1
C.
D.
-3
922
0
5
3
a33
X1 =
1
λ₁ = -2,
X2 =
1
A. (-) Find the values of a11, a22, and a23 such that X₁ is an eigenvector of matrix A and 2₁ is
the corresponding eigenvalues.
) Given the other 2 eigenvectors, X₁ and X2, find the remaining two eigenvalues, λ₁ and ₂,
of A.
X3 = 8
[3]
) Based on your answers from part A and part B, state why matrix A is diagonalizable.
Write down the matrix of eigenvectors X = [X₁, X2, X3] and the diagonalization matrix A.
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