A latex example:
<latex>
The characteristic polynomial $f(\lambda)$ of the
$3 \times 3$ matrix
\[
\left(
\begin{array}{ccc}
a & b & c
d & e & f
g & h & i \end{array}
\right)\]
is given by the equation
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c
-d & \lambda - e & -f
-g & -h & \lambda - i \end{array}
\right|.\]
</latex>
<latex>
(3x - 3y + 2z = 11)+(-1(3x + y - 3z = 11))=> -4y + 5z = 0
</latex>
another example
<latex>
\frac{3}{4 \pi} \sqrt{4 \cdot x^2 12}\\
\lim_{n \to \infty}
\sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\\
\it{f}(x) = \frac{1}{\sqrt{x} x^2}\\
e^{i \pi} + 1 = 0\;
</latex>
Some more latex:
<latex>
$ \begin{align*}
\int x^2 dx & = \frac{1}{3}x^3
\therefore\quad\int_0^1 x^2 dx &= \frac{1}{3}
\end{align*}
$
</latex>
And some more:
<latex>
\begin{tabular}{|l|l|p{9cm}|}
\hline
option & variants & explanation
\hline
id & unique string & Identifies the user uniquely.
\hline
logmask & ALL & Log everything
\cline{2-3}
& DBG & Log only debug
\cline{2-3}
& WARN & Log only warning messages
\hline
printTID & flag & Print Thread ID or not.
\hline
prefix & any string & With this will be prefixed all messages of this user.
\hline
p & p & p
\hline
p & p & p
\hline
p & p & p
\hline
p & p & p
\hline
\end{tabular}
</latex>