WeBWorK Standalone Renderer

This is the first part of a two-part problem.

Rewrite the given system of linear homogeneous differential equations as a homogeneous linear system of the form $\boldsymbol{\vec{y}^{\,\prime}} = P \boldsymbol{\vec{y}}$ .

$\begin{array}{rcl} y_1^{\,\prime} & = & 2y_1 + y_2 + y_3, \\ y_2^{\,\prime} & = & y_2 + 2y_3 + y_1, \\ y_3^{\,\prime} & = & 2y_2 + y_1 + y_3. \end{array}$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$	$y_1^{\,\prime}$	$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
	$y_2^{\,\prime}$
	$y_3^{\,\prime}$

=

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

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$	$y_1$	$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
	$y_2$
	$y_3$