# Toronto Math Forum

## MAT244--2018F => MAT244--Tests => Quiz-6 => Topic started by: Victor Ivrii on November 17, 2018, 03:49:22 PM

Title: Q6 TUT 0101
Post 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.
$$\mathbf{x}' =\begin{pmatrix} \frac{5}{4} &\frac{3}{4}\\ \alpha & \frac{5}{4} \end{pmatrix}\mathbf{x}.$$
Title: Re: Q6 TUT 0101
Post by: Qing Zong on November 17, 2018, 04:55:24 PM
This is my solution
Title: Re: Q6 TUT 0101
Post by: Jiacheng Ge on November 18, 2018, 12:57:01 PM