Suppose A is a 2 x 2 real matrix that has two eigenvalues A₁ and ₂, and X₁ is not equal to X₂. Matrix A is also symmetric, and an eigenvector of A corresponding to eigenvalue X₁ is v₁ = [4] If the eigenvector for eigenvalue X₂ is What does k need to be equal to? v2 =
Suppose A is a 2 x 2 real matrix that has two eigenvalues A₁ and ₂, and X₁ is not equal to X₂. Matrix A is also symmetric, and an eigenvector of A corresponding to eigenvalue X₁ is v₁ = [4] If the eigenvector for eigenvalue X₂ is What does k need to be equal to? v2 =
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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![Suppose \( A \) is a \( 2 \times 2 \) real matrix that has two eigenvalues \( \lambda_1 \) and \( \lambda_2 \), and \( \lambda_1 \) is not equal to \( \lambda_2 \). Matrix \( A \) is also symmetric, and an eigenvector of \( A \) corresponding to eigenvalue \( \lambda_1 \) is \( v_1 = \begin{bmatrix} 5 \\ -4 \end{bmatrix} \).
If the eigenvector for eigenvalue \( \lambda_2 \) is
\[ v_2 = \begin{bmatrix} k \\ 1 \end{bmatrix} \]
What does \( k \) need to be equal to?
[Here there would be a text box or some input field for the user to provide their answer.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b609ed5-0879-4e23-8eee-4515e84ef2b9%2F9e8a357b-ecbd-409f-8c4a-8288879c4ec3%2Flp868f_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose \( A \) is a \( 2 \times 2 \) real matrix that has two eigenvalues \( \lambda_1 \) and \( \lambda_2 \), and \( \lambda_1 \) is not equal to \( \lambda_2 \). Matrix \( A \) is also symmetric, and an eigenvector of \( A \) corresponding to eigenvalue \( \lambda_1 \) is \( v_1 = \begin{bmatrix} 5 \\ -4 \end{bmatrix} \).
If the eigenvector for eigenvalue \( \lambda_2 \) is
\[ v_2 = \begin{bmatrix} k \\ 1 \end{bmatrix} \]
What does \( k \) need to be equal to?
[Here there would be a text box or some input field for the user to provide their answer.]
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