MAT244--2018F > Quiz-6

Q6 TUT 0101

(1/1)

Victor Ivrii:
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.
$$\mathbf{x}' =\begin{pmatrix} \frac{5}{4} &\frac{3}{4}\\ \alpha & \frac{5}{4} \end{pmatrix}\mathbf{x}.$$

Qing Zong:
This is my solution

Jiacheng Ge: