For the system of ODEs shown below, determine the followings: 10 \frac{d x}{d t}=4 x-4 y 20 \frac{d y}{d t}=4 x-8 y ) The above system can be rewritten in matrix form as \dot{\mathbf{x}}=A \mathbf{x} where x is the vector with solutions: \mathbf{x}=\left[\begin{array}{l}

x(t) \\

y(t)

\end{array}\right] Write down the system matrix A. -) Calculate the eigenvalues of the system matrix A. Calculate the eigenvectors of the system matrix A. d)Write down the general solutions for x(t) and y(t) e) Comment on the modes.