\documentclass[a4paper,11pt]{report}
\usepackage[latin1]{inputenc}
\usepackage[italian]{babel}
\usepackage{graphicx}

\newtheorem{prop}{Proposizione}
\newtheorem{defin}{Definizione}
\newtheorem{oss}{Osservazione}
\newtheorem{ese}{Esempio}


\begin{document}


\begin{ese}
$\mathcal C:5x^2+y^2+2xy+4x+6y+1=0$, ha come matrici
$$
\mathrm A=\left(
\begin{array}{ccc}
 5 & 1 & 2\\
 1 & 1 & 3\\
 2 & 3 & 1
\end{array}
\right) \qquad \mathrm A_0=\left(
\begin{array}{cc}
5 & 1\\
1 & 1
\end{array}
\right)
$$
$\mathcal C:x^2+\pi y^2+2\sqrt{2}xy+8y=1$, ha come matrici
$$
\mathrm A=\left(
\begin{array}{ccc}
1 & \sqrt 2 & 0 \\
\sqrt 2 & \pi & 4\\
 0 & 4 & -1
\end{array}
\right) \qquad \mathrm A_0=\left(
\begin{array}{cc}
 1 & \sqrt 2\\
\sqrt 2 & \pi
\end{array}
\right)
$$
$\mathcal C:\alpha x^2=2\gamma y$, ha come matrici
$$
\mathrm A=\left(
\begin{array}{rrr}
 \alpha & 0 & 0\\
 0 & 0 &-\gamma \\
 0 & -\gamma& 0
\end{array}
\right) \qquad \mathrm A_0=\left(
\begin{array}{cc}
 \alpha & 0\\
  0& 0
\end{array}
\right).
$$
\end{ese}

\end{document}
