Difference between revisions of "AoPS Wiki:Sandbox"
Lowtopology (talk | contribs) (→Sandbox Area) |
Lowtopology (talk | contribs) (→Sandbox Area) |
||
Line 23: | Line 23: | ||
<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
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
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array}
\right|.\]