A matrix A has the following eigenpairs. (₁-4. [²]) (-². [H]) = 2, Use these eigenpairs to find matrix A. Hint: A = PDP-1 A = = 6 Ex: 5
A matrix A has the following eigenpairs. (₁-4. [²]) (-². [H]) = 2, Use these eigenpairs to find matrix A. Hint: A = PDP-1 A = = 6 Ex: 5
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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![A matrix \( A \) has the following eigenpairs:
\[ \left( \lambda_1 = 4, \begin{bmatrix} 2 \\ 1 \end{bmatrix} \right) \quad \left( \lambda_2 = 2, \begin{bmatrix} 1 \\ 1 \end{bmatrix} \right) \]
Use these eigenpairs to find matrix \( A \). Hint: \( A = PDP^{-1} \).
\[ A = \begin{bmatrix} 6 & \, \, \\ \text{Ex: 5} & \, \, \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97fa71a9-ddb9-496b-9b0a-bf970e388fad%2F3ee5118f-837a-492a-934c-07de2cf5f2ff%2Fvpsh3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A matrix \( A \) has the following eigenpairs:
\[ \left( \lambda_1 = 4, \begin{bmatrix} 2 \\ 1 \end{bmatrix} \right) \quad \left( \lambda_2 = 2, \begin{bmatrix} 1 \\ 1 \end{bmatrix} \right) \]
Use these eigenpairs to find matrix \( A \). Hint: \( A = PDP^{-1} \).
\[ A = \begin{bmatrix} 6 & \, \, \\ \text{Ex: 5} & \, \, \end{bmatrix} \]
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