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Consider the following two-dimensional linear dynamical system, dx₁ dt dx2 dt 10 8 - · (²8_ _30) (2¹). -8 -10, 1. What is the trace and determinant of this system? 2. Find the eigen values and eigen vectors. (x₁(t)` of the system. (x₂(t), 3. Write the solution

Consider the following two-dimensional linear dynamical system, dx₁ dt dx2 dt 10 8 - · (²8_ _30) (2¹). -8 -10, 1. What is the trace and determinant of this system? 2. Find the eigen values and eigen vectors. (x₁(t)` of the system. (x₂(t), 3. Write the solution

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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Consider the following two-dimensional linear dynamical system, dx₁ dt dx2 dt = 10 (¹8_-30) (2¹1) 1. What is the trace and determinant of this system? 2. Find the eigen values and eigen vectors. 'x₁(t)` x₂ (t) 4. Sketch the phase portrait for this system. 5. Write the equivalent second order differential 1D equation for the 2D first order system above. 6. Evaluate the contour integral I = f d0 = ArcTan (1/2), and C is do a circle of radius 1 centered at the origin. What is the value I which you have just computed called? 3. Write the solution of the system.
Transcribed Image Text:Consider the following two-dimensional linear dynamical system, dx₁ dt dx2 dt = 10 (¹8_-30) (2¹1) 1. What is the trace and determinant of this system? 2. Find the eigen values and eigen vectors. 'x₁(t)` x₂ (t) 4. Sketch the phase portrait for this system. 5. Write the equivalent second order differential 1D equation for the 2D first order system above. 6. Evaluate the contour integral I = f d0 = ArcTan (1/2), and C is do a circle of radius 1 centered at the origin. What is the value I which you have just computed called? 3. Write the solution of the system.
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Trace of a square matrix is the sum of the elements in principal diagonal.

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