Rewrite the second order differential equation $$u'' + 3 u' + 6 u = 0$$ as an equivalent system of first order differential equations. In your answers use the single letter u to represent the function $u$ and the single letter v to represent the "velocity function" $u'$. Do not use $u(t)$ or $v(t)$. This problem only asks you to rewrite the differential equation; do not solve it.

$u' =$
$v' =$

Now rewrite the first order system using matrices:

$\displaystyle \frac{d}{dt}$

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

$=$

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

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

.