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A matrix A has the following eigenpairs. (₁₁ 4. [²]) (¹₂=². []) = 2, Use these eigenpairs to find matrix A. Hint: A = PDP-¹

A matrix A has the following eigenpairs. (₁₁ 4. [²]) (¹₂=². []) = 2, Use these eigenpairs to find matrix A. Hint: A = PDP-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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**Eigenpairs of Matrix A:** A matrix \( A \) has the following eigenpairs: 1. \( (\lambda_1 = 4, \begin{bmatrix} 2 \\ 1 \end{bmatrix}) \) 2. \( (\lambda_2 = 2, \begin{bmatrix} 1 \\ 1 \end{bmatrix}) \) **Task:** Use these eigenpairs to find matrix \( A \). **Hint:** The matrix \( A \) can be found using the formula \( A = PDP^{-1} \). **Matrix Representation:** \[ A = \begin{bmatrix} 6 & \text{Ex: 5} \\ & \end{bmatrix} \]
Transcribed Image Text:**Eigenpairs of Matrix A:** A matrix \( A \) has the following eigenpairs: 1. \( (\lambda_1 = 4, \begin{bmatrix} 2 \\ 1 \end{bmatrix}) \) 2. \( (\lambda_2 = 2, \begin{bmatrix} 1 \\ 1 \end{bmatrix}) \) **Task:** Use these eigenpairs to find matrix \( A \). **Hint:** The matrix \( A \) can be found using the formula \( A = PDP^{-1} \). **Matrix Representation:** \[ A = \begin{bmatrix} 6 & \text{Ex: 5} \\ & \end{bmatrix} \]
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Step 1: Introduction of the given problem

lambda subscript 1 equals 4 and corresponding eigen vector is open square brackets table row 2 row 1 end table close square brackets

lambda subscript 2 equals 2 and corresponding eigen vector is open square brackets table row 1 row 1 end table close square brackets

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