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Consider the following system. dx § = C1§(¹) + C₂§(²) dt = C1 -3 - (39) 0 -3 Find the eigenvalues and the corresponding eigenvectors. Number of distinct eigenvalues: Choose one (3) X +0₂ (?)

Consider the following system. dx § = C1§(¹) + C₂§(²) dt = C1 -3 - (39) 0 -3 Find the eigenvalues and the corresponding eigenvectors. Number of distinct eigenvalues: Choose one (3) X +0₂ (?)

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 system. dx dt Find the eigenvalues and the corresponding eigenvectors. Number of distinct eigenvalues: Choose one { = C₁(¹) + C₂ (²) = C1 (?) where (¹) and (2) are eige ( )x -3 0 0 -3 +0₂ (?) Choose one an asymptotically stable proper node an unstable proper node Classify the critical point is stable, asymptotically st an asymptotically stable improper node The critical point (0,0) is an unstable improper node a stable spiral
Transcribed Image Text:Consider the following system. dx dt Find the eigenvalues and the corresponding eigenvectors. Number of distinct eigenvalues: Choose one { = C₁(¹) + C₂ (²) = C1 (?) where (¹) and (2) are eige ( )x -3 0 0 -3 +0₂ (?) Choose one an asymptotically stable proper node an unstable proper node Classify the critical point is stable, asymptotically st an asymptotically stable improper node The critical point (0,0) is an unstable improper node a stable spiral
Consider the following system. dx ( )₁ -3 0 0 -3 X dt Find the eigenvalues and the corresponding eigenvectors. Number of distinct eigenvalues: Choose one { = C₁(¹) + C₂ (²) = C₁ (3) +02 (?) where (¹) and (2) are eigenvectors; c₁ and c₂ are arbitrary constants. Classify the critical point (0, 0) as to type and determine whether it is stable, asymptotically stable, or unstable. The critical point (0,0) is [Choose one
Transcribed Image Text:Consider the following system. dx ( )₁ -3 0 0 -3 X dt Find the eigenvalues and the corresponding eigenvectors. Number of distinct eigenvalues: Choose one { = C₁(¹) + C₂ (²) = C₁ (3) +02 (?) where (¹) and (2) are eigenvectors; c₁ and c₂ are arbitrary constants. Classify the critical point (0, 0) as to type and determine whether it is stable, asymptotically stable, or unstable. The critical point (0,0) is [Choose one
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