Chapter 7: Problem 20
The coefficient matrix contains a parameter \(\alpha\). In each of these problems: (a) Determine the eigervalues in terms of \(\alpha\). (b) Find the critical value or values of \(\alpha\) where the qualitative nature of the phase portrait for the system changes. (c) Draw a phase portrait for a value of \(\alpha\) slightly below, and for another value slightly above, each crititical value. $$ x^{\prime}=\left(\begin{array}{cc}{4} & {\alpha} \\ {8} & {-6}\end{array}\right) \mathbf{x} $$