Consider the dynamical system:
\begin{array} \frac{dx}{dt}=-5x+y\\ \frac{dy}{dt}=-125x+15y \end{array}
a)
The system can be written in the form \frac{dx}{dt}=Ax, where x=\binom{x}{y}.
Identify the components of the matrix A:
A = \begin{pmatrix} \input & \input \\ \input & \input \end{pmatrix}
b)
Calculate the trace, \tau, and the determinant, \delta, of the matrix A:
\begin{array} \tau=\input \\ \delta=\input \end{array}
c)
Enter the eigenvalues, \lambda_1 and \lambda_2, of the matrix A:
If the eigenvalues have zero imaginary part, enter the eigenvalue with the largest real part first.
If the eigenvalues have non-zero imaginary part, enter the eigenvalue with the largest imaginary part first.
\begin{array} \lambda_1=\input \\ \lambda_2=\input \end{array}