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>