Given the following, -3 5 -B:) -0 -1 a22 3 X1 = 1 -3 0 a33 C. D. A = λ₁ = -2, 3 20, 2012:01: A. ) Find the values of a11, 922, and a23 such that x₁ is an the corresponding eigenvalues. B. Given the other 2 eigenvectors, x of A. X3 = 8 [3] eigenvector of matrix A and ₁ is such that x₁ is an eigenvector of matrix A and 2₁ is and x₂, find the remaining two eigenvalues, A₁ and 22, 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.
Given the following, -3 5 -B:) -0 -1 a22 3 X1 = 1 -3 0 a33 C. D. A = λ₁ = -2, 3 20, 2012:01: A. ) Find the values of a11, 922, and a23 such that x₁ is an the corresponding eigenvalues. B. Given the other 2 eigenvectors, x of A. X3 = 8 [3] eigenvector of matrix A and ₁ is such that x₁ is an eigenvector of matrix A and 2₁ is and x₂, find the remaining two eigenvalues, A₁ and 22, 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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![Given the following,
A.
[911
-3
5
A = -1 922 3
1-3 0 a33
C.
D.
X₁ = 1
) Find the values of a11, 922, and a23 such that x₁ is an eigenvector of matrix A and 2₁ is
such that x₁ is an eigenvector of matrix A and 2₁ is
the corresponding eigenvalues.
B. Given the other 2 eigenvectors, x₁ and x₂, find the remaining two eigenvalues, λ₁ and 2₂,
.
λ₁ = -2,
X2
X3 = 8
- A
13.
11/2012 2:01:11
Based on your answers from part A and part B, state why matrix A is diagonalizable.
J Write
the matrix of eigenvectors X = [X₁, X2, X3] and the diagonalization matrix A.
afa down](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F547803a6-40ba-407b-9edd-fe79ffc19960%2F3f31a25f-e84c-4be6-8c79-a47d307cd515%2Futxg7hf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the following,
A.
[911
-3
5
A = -1 922 3
1-3 0 a33
C.
D.
X₁ = 1
) Find the values of a11, 922, and a23 such that x₁ is an eigenvector of matrix A and 2₁ is
such that x₁ is an eigenvector of matrix A and 2₁ is
the corresponding eigenvalues.
B. Given the other 2 eigenvectors, x₁ and x₂, find the remaining two eigenvalues, λ₁ and 2₂,
.
λ₁ = -2,
X2
X3 = 8
- A
13.
11/2012 2:01:11
Based on your answers from part A and part B, state why matrix A is diagonalizable.
J Write
the matrix of eigenvectors X = [X₁, X2, X3] and the diagonalization matrix A.
afa down
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