Toronto Math Forum
MAT2442018F => MAT244Tests => Quiz6 => Topic started by: Victor Ivrii on November 17, 2018, 03:49:22 PM

The coefficient matrix contains a parameter $\alpha$.
(a) Determine the eigenvalues 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 critical value.
$$\mathbf{x}' =\begin{pmatrix}
\frac{5}{4} &\frac{3}{4}\\
\alpha & \frac{5}{4}
\end{pmatrix}\mathbf{x}.$$

This is my solution

My answer is different.

Both solutions are barely readable (one due to poor handwriting, second due to making crappy snapshot instead of scanning). The second is complete, but one should explain how "it is different".