Difference between revisions of "AoPS Wiki:Sandbox"
Lowtopology (talk | contribs) (→Sandbox Area) |
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<math>\lim_{x\to0}\frac{a}{x}</math> | <math>\lim_{x\to0}\frac{a}{x}</math> | ||
| + | |||
| + | The characteristic polynomial <math>f(\lambda)</math> of the | ||
| + | <math>3 \times 3</math> matrix | ||
| + | \[ | ||
| + | \left( | ||
| + | \begin{array}{ccc} | ||
| + | a & b & c \\ | ||
| + | d & e & f \\ | ||
| + | g & h & i \end{array} | ||
| + | \right)\] | ||
| + | is given by the equation | ||
| + | \[ f(\lambda) | ||
| + | = \left| | ||
| + | \begin{array}{ccc} | ||
| + | \lambda - a & -b & -c \\ | ||
| + | -d & \lambda - e & -f \\ | ||
| + | -g & -h & \lambda - i \end{array} | ||
| + | \right|.\] | ||
Revision as of 08:20, 12 June 2009
Welcome to the sandbox, a location to test your newfound wiki-editing abilities.
Please note that all contributions here may be deleted periodically and without warning.
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
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array}
\right|.\]
