1. Find the most general real-valued solution to the linear system of differential equations $\displaystyle \boldsymbol{\vec{x}^{\, \prime}} = \left\lbrack \begin{array}{rr} 0 & -1 \\ 9 & 0 \end{array} \right\rbrack \boldsymbol{\vec{x}}.$
   
   

   $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $x_1(t)$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $x_2(t)$

   $= c_1$

   $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

   $+ \ c_2$

   $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

   
   
   
2. In the phase plane, this system is best described as a
   source / unstable node
   sink / stable node
   saddle
   center point / ellipses
   spiral source
   spiral sink
   none of these