Difference between revisions of "AoPS Wiki:Sandbox"
Lowtopology (talk | contribs) (→Sandbox Area) |
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The characteristic polynomial <math>f(\lambda)</math> of the | The characteristic polynomial <math>f(\lambda)</math> of the | ||
<math>3 \times 3</math> matrix | <math>3 \times 3</math> matrix | ||
| − | + | <math> | |
\left( | \left( | ||
\begin{array}{ccc} | \begin{array}{ccc} | ||
| Line 32: | Line 32: | ||
d & e & f \\ | d & e & f \\ | ||
g & h & i \end{array} | g & h & i \end{array} | ||
| − | \right) | + | \right)</math> |
is given by the equation | is given by the equation | ||
| − | + | <math> f(\lambda) | |
= \left| | = \left| | ||
\begin{array}{ccc} | \begin{array}{ccc} | ||
| Line 40: | Line 40: | ||
-d & \lambda - e & -f \\ | -d & \lambda - e & -f \\ | ||
-g & -h & \lambda - i \end{array} | -g & -h & \lambda - i \end{array} | ||
| − | \right|. | + | \right|.</math> |
Revision as of 07:21, 12 June 2009
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
is given by the equation
