## Complex Eigenvalues and systems of 1st-order ODEs February 12 2

I am trying to solve $\begin{aligned} \dfrac{dx}{dt} &= x+ y \\ \dfrac{dy}{dt} &= -10 x- y \end{aligned}$.My strategy is to let $P = \left[\begin{array}{cc} 1 &1\cr -10 & -1 \end{array}\right]$ and find $\det(P - \lambda I) = 0 $ and I get