AoPS Wiki:Sandbox: Difference between revisions
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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 07:20, 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.
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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
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array}
\right|.\]
