Suppose a system of constant coefficient differential equations \(\dot{\vec{x}} = A \vec{x}\) has a \(2 \times 2\) matrix \(A\) with eigenvalues \(\lambda_1, \lambda_2 = 2 \pm 6i\) and \(\lambda_1 = 2 + 6i\) has eigenvector \(\begin{bmatrix} 1 \\ -1 + i \end{bmatrix}\). Find the real part \(\vec{x}_1\) and the imaginary part \(\vec{x}_2\) and write the fundamental matrix \([\vec{x}_1 \ \vec{x}_2]\) for the general solution: [Empty Boxes](Note: The text provides a mathematical description of finding the real and imaginary parts of a solution related to a given complex eigenvalue and eigenvector, used for constructing the general solution of a differential equation system.)

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Answered: Suppose a system of constant…

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 system of constant coefficient differential equations - Az has a 2 x 2 matrix A with Find the real part ₁ and the eigenvalues A1, A2 = 2 ±6i and A₁ = 2 + 6i has eigenvector [1+1 1+ imaginary part ₂ and write the fundamental matrix [1 2] for the general solution: