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:
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.
As we clearly now that,
Hence, the final answer is:
25: Consider a positive transition matrix
meaning that a, b, c, and d are positive numbers such that a + c = b + d = 1. (The matrix in Exercise 24 has this form.) Verify that
are eigenvectors of A. What are the associated eigenvalues? Is the absolute value of these eigenvalues more or less than 1?
Sketch a phase portrait.
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