this question below Suppose a system of constant coefficient differential equations '= A has a 2 x 2 matrix A with 1 . Find the real part ₁ and the -5+6i] eigenvalues A1, A2 = 4±2i and A₁ = 4+2i has eigenvector imaginary part 2 and write the fundamental matrix [₁2] for the general solution: Submit Question 1 x -5 x 0x 6 x
this question below Suppose a system of constant coefficient differential equations '= A has a 2 x 2 matrix A with 1 . Find the real part ₁ and the -5+6i] eigenvalues A1, A2 = 4±2i and A₁ = 4+2i has eigenvector imaginary part 2 and write the fundamental matrix [₁2] for the general solution: Submit Question 1 x -5 x 0x 6 x
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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![**Educational Website Content: Differential Equations and Eigenvalues**
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**Topic: System of Constant Coefficient Differential Equations**
Suppose a system of constant coefficient differential equations \( \mathbf{x}' = A\mathbf{x} \) has a 2 x 2 matrix \( A \) with eigenvalues \( \lambda_1, \lambda_2 = 4 \pm 2i \) and \( \lambda_1 = 4 + 2i \) has eigenvector \( \begin{bmatrix} 1 \\ -5 + 6i \end{bmatrix} \).
Find the real part \( \mathbf{x}_1 \) and the imaginary part \( \mathbf{x}_2 \), and write the fundamental matrix \( [\mathbf{x}_1 \ \mathbf{x}_2] \) for the general solution:
**Input Fields:**
- Real part input: Enter a 1 in the first box and 0 in the second box for \( \mathbf{x}_1 \).
- Imaginary part input: Enter -5 in the first box and 6 in the second box for \( \mathbf{x}_2 \).
[Submit Question Button]
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The form above provides a way to input the real and imaginary parts of the eigenvector corresponding to the given complex eigenvalues, helping students practice constructing the fundamental matrix for solving differential equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4100c518-1a8f-4898-88a2-d0f1a7669694%2F49f8663c-b883-452a-a3b3-4e9a0a51cf4d%2F3s14qwt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Differential Equations and Eigenvalues**
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**Topic: System of Constant Coefficient Differential Equations**
Suppose a system of constant coefficient differential equations \( \mathbf{x}' = A\mathbf{x} \) has a 2 x 2 matrix \( A \) with eigenvalues \( \lambda_1, \lambda_2 = 4 \pm 2i \) and \( \lambda_1 = 4 + 2i \) has eigenvector \( \begin{bmatrix} 1 \\ -5 + 6i \end{bmatrix} \).
Find the real part \( \mathbf{x}_1 \) and the imaginary part \( \mathbf{x}_2 \), and write the fundamental matrix \( [\mathbf{x}_1 \ \mathbf{x}_2] \) for the general solution:
**Input Fields:**
- Real part input: Enter a 1 in the first box and 0 in the second box for \( \mathbf{x}_1 \).
- Imaginary part input: Enter -5 in the first box and 6 in the second box for \( \mathbf{x}_2 \).
[Submit Question Button]
---
The form above provides a way to input the real and imaginary parts of the eigenvector corresponding to the given complex eigenvalues, helping students practice constructing the fundamental matrix for solving differential equations.
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