a. Find the eigenvalues and eigenvectors of the matrix $\begin{bmatrix} -1 & -6\\ 0 & -7 \end{bmatrix}$.
$\lambda_1 = -7$, $v_1 = \begin{bmatrix} 1\\ 1 \end{bmatrix}$, and $\lambda_2 = -1$, $v_2 = \begin{bmatrix} 1\\ 0 \end{bmatrix}$
b. Solve the system of differential equations $Y' = \begin{bmatrix} -1 & -6\\ 0 & -7 \end{bmatrix} Y$
satisfying the initial conditions $\begin{bmatrix} y_1(0)\\ y_2(0) \end{bmatrix} = \begin{bmatrix} 1\\ -1 \end{bmatrix}$.
$y_1(t) =
$
y_2(t) =
