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}