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| − | {{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line -->
| + | =A= |
| − | In the computer world, a '''sandbox''' is a place to test and experiment -- essentially, it's a place to play.
| + | ==B== |
| − | | + | ===C=== |
| − | This is the AoPSWiki Sandbox. Feel free to experiment here.
| + | ====E==== |
| − | | + | Apple |
| − | Warning: anything you place here is subject to deletion without notice.
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| − | | |
| − | === Sandbox Area === | |
| − | <asy>
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| − | draw((0,0)--(3,9),black);
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| − | label("$71^\circ$",(0,0),NE);
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| − | draw((3,9)--(6,0),black);
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| − | label("$71^\circ$",(6,0),NW);
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| − | draw((0,0)--(6,0),black);
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| − | label("$38^\circ$",(3,8),S);
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| − | dot((0,0));
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| − | dot((3,9));
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| − | dot((6,0));
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| − | draw((-1,7)--(2.3,5.9),black);
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| − | draw((-1,6)--(2,6),red);
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| − | label("$19^\circ$",(1,6),NW);
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| − | </asy>
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| − | | |
| − | <math>\lim_{x\to0}\frac{a}{x}</math>
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| − | | |
| − | The characteristic polynomial <math>f(\lambda)</math> of the
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| − | <math>3 \times 3</math> matrix
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| − | <math>
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| − | \left(
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| − | \begin{array}{ccc}
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| − | a & b & c \\
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| − | d & e & f \\
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| − | g & h & i \end{array}
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| − | \right)</math>
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| − | is given by the equation
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| − | <math> f(\lambda)
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| − | = \left| | |
| − | \begin{array}{ccc}
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| − | \lambda - a & -b & -c \\
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| − | -d & \lambda - e & -f \\
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| − | -g & -h & \lambda - i \end{array}
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| − | \right|.</math>
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