AoPS Wiki:Sandbox
Template:AoPSWiki:Sandbox/header In the computer world, a sandbox is a place to test and experiment -- essentially, it's a place to play.
This is the AoPSWiki Sandbox. Feel free to experiment here.
Warning: anything you place here is subject to deletion without notice.
Sandbox Area
![[asy] draw((0,0)--(3,9),black); label("$71^\circ$",(0,0),NE); draw((3,9)--(6,0),black); label("$71^\circ$",(6,0),NW); draw((0,0)--(6,0),black); label("$38^\circ$",(3,8),S); dot((0,0)); dot((3,9)); dot((6,0)); draw((-1,7)--(2.3,5.9),black); draw((-1,6)--(2,6),red); label("$19^\circ$",(1,6),NW); [/asy]](http://latex.artofproblemsolving.com/3/4/9/349e45904453e378fffc7cf94a55247ad2cc73f3.png)
The characteristic polynomial 
of the
matrix
\[
\left(
\begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \end{array}
\right)\]
is given by the equation
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array}
\right|.\]
