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System of Equations : Matrix Form and Eigenvalues

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Consider the attached system of equations.

(a) Write the system in the given matrix form {see attachment}
(b) Determine the eigenvalues of A in terms of the parameter {see attachment}
(c) The qualitative nature of solutions depends on ....
(d) Sketch a typical phase portrait...

Please see attachment for complete set of questions. Also, please note: no computer, no calculator. Show how you would have done things by hand. Thanks!

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Solution Summary

A system of equations is investigated. Phase Portraits are shown. The solution is detailed and well presented.

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