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Linear Algebra With Applications
Found in: Page 336
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

26: Based on your answers in Exercises 24 and 25, sketch a phase portrait of the dynamical system


Phase portrait of a dynamical system is: Atx0=0.25tα+0.25β-0.25tα+0.5β

See the step by step solution

Step by Step Solution

Step 1: Transition Matrix

Transition matrix may refer to: The matrix associated with a change of basis for a vector space. Stochastic matrix, a square matrix used to describe the transitions of a Markov chain. State-transition matrix, a matrix whose product with the state vector at an initial time gives state vector at that time.

Step 2: Sketching a phase portrait of the dynamical system:

As we clearly now that,


role="math" localid="1659584611493" x0=α1-1+β0.250.5Atx0=0.25tα1-1+β0.250.5=0.25tα+0.25β-0.25tα+0.5β

Hence, the final answer is: Atx0=0.25tα+0.25β-0.25tα+0.5β

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