Consider the systemx =1 1 1x.(a) Solve the system for = 0.5. What are the eigenvalues of
Chapter 7, Problem 31(choose chapter or problem)
Consider the systemx =1 1 1x.(a) Solve the system for = 0.5. What are the eigenvalues of the coefficient matrix?Classify the equilibrium point at the origin as to type.(b) Solve the system for = 2.What are the eigenvalues of the coefficient matrix? Classifythe equilibrium point at the origin as to type.(c) In parts (a) and (b), solutions of the system exhibit two quite different types of behavior.Find the eigenvalues of the coefficient matrix in terms of , and determine the valueof between 0.5 and 2 where the transition from one type of behavior to the other occurs.
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