\documentclass[11pt]{article}

 \usepackage{ifthen}

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 % \usepackage{fourier}

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  \usepackage{geometry}
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 % \setenumerate{align=left,leftmargin=*,noitemsep}
\setenumerate{align=left,leftmargin=*}
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  \usepackage[np]{numprint}

  \usepackage[official,right]{eurosym}
  \usepackage[frenchb]{babel}
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  \DecimalMathComma

\newcounter{exercice}
\newcounter{refex}
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\newcounter{partie}[exercice]
\newcounter{refpart}
\renewcommand{\thepartie}{\Alph{partie}}
\renewcommand{\therefpart}{\Alph{partie}}

\makeatletter
\newenvironment{exercice}[1][]{%
		     \stepcounter{exercice}
		     \refstepcounter{refex}
		     \vspace{0.5em}
		     \par
                     \def\@svsechd{\large \color{white} \colorbox{purple}{\bfseries\arabic{exercice}}}%
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                     \ifthenelse{\equal{#1}{}}{}{\textbf{#1}\par}%
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\makeatother

\newenvironment{partie}[1][]{%
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		      \par \vspace{0.5ex}\noindent
		     \textbf{Partie \thepartie \ifthenelse{\equal{#1}{}}{}{\quad -\quad#1}%
		     }\nopagebreak\par%
                     }{\par\vspace{1em}}



%%%%%%%%%%% Ensembles %%%%%%%%%%%%
\newcommand{\D}{\mathbb{D}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}

%%%%%%%%%%% Intervalles %%%%%%%%%%%%
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\newcommand{\intervalleOF}[2]{\left]{#1}\,{;}\,{#2}\right]}
\newcommand{\intervalleFO}[2]{\left[{#1}\,{;}\,{#2}\right[}
\newcommand{\intervalleFF}[2]{\left[{#1}\,{;}\,{#2}\right]}

\newcommand{\couple}[2]{\left(#1\,{;}\,{#2}\right)}


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\newcommand{\cald}{\mathscr{D}}

%%%%%%%%%%%% Vecteurs %%%%%%%%%%%%%%%
\usepackage[e]{esvect}
\newcommand{\vect}[1]{\vv{#1}}
\newcommand{\repere}[3]{\left(#1\,{;}\,\vect{#2}{,}\,\vect{#3} \right)}
\newcommand{\oij}{\repere{O}{\imath}{\jmath}}
\newcommand{\barre}[1]{\overline{#1\rule{0.1em}{0ex}}}

%%%%%%%%%%%% Coordonnées %%%%%%%%%%%%%%%
\newcommand{\cp}[2]{%
        \begin{pmatrix}
        #1\\
        #2
        \end{pmatrix}%
        }

%%%%%%%%%%%% Systèmes %%%%%%%%%%%%%%%
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       \left\{
       \begin{aligned}
          #1\\
          #2\\
       \end{aligned}
       \right.%
       }

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       \begin{aligned}
          #1\\
          #2\\
	  #3
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\newcommand{\sysq}[4]{%
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       \begin{aligned}
          #1\\
          #2\\
	  #3
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       \right.%
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%%%%%%%%%%%% Divers %%%%%%%%%%%%%%%
\DeclareMathOperator{\card}{Card}


% perso nico

\newcommand{\orth}{\bot} % Pour faire le symbole perpendiculaire
\newcommand{\cm}{\,\mathrm{cm}} 
\newcommand{\pI}{{\ensuremath{+\infty}}} 
\newcommand{\mI}{{\ensuremath{-\infty}}} 

\newcommand{\cala}{\mathscr{A}}
\newcommand{\calb}{\mathscr{B}}
\newcommand{\calp}{\mathscr{P}}
\newcommand{\cale}{\mathscr{E}}
\newcommand{\calf}{\mathscr{F}}
\newcommand{\cals}{\mathscr{S}}
\newcommand{\calh}{\mathscr{H}}




\newcommand{\ssi}{\Longleftrightarrow} % Pour faire le symbole equivalent
\newcommand{\implique}{\Longrightarrow} % Pour faire le symbole implique

\usepackage{enumitem}
\usepackage{xypic}

  \usepackage{amsmath}
  \usepackage{amssymb}
  \usepackage{amsfonts}
  \usepackage{mathrsfs}
%  \usepackage{shortlst}


\usepackage{pstricks,pst-plot,pst-text,pst-tree,pst-eps,pst-fill,pst-node,pst-math}

\newtheorem{remarque}{Remarque}
\newtheorem{remarque*}{Remarque}
\newtheorem{theorem*}{Théorème}

% --------------------------------------------------------------------------------------------------

%devoir surveillé personalisé
% #1 titre principal, #2 titre milieu haut en petit, #3 titre haut
% gauche, #4 titre haut droit 
\newcommand{\devpers}[4]{
                         %\pagestyle{empty} 
                         \noindent 
                         \begin{minipage}[t]{\linewidth}
                         \textit{#3 } \hfill \textit{ #2} \hfill \textit{#4}
                         \end{minipage}
                         \begin{center}{{\Large\bf #1 }} \end{center} 
                         \vspace{-0.3cm}
                         \rule{\linewidth}{0.5mm} 
                         }

\pagestyle{empty} 
\begin{document}

\devpers{Prueba 2 : sistemas de ecuaciones, determinantes}{}{TS,\ 15 de octubre 2014}{}


\begin{exercice}
 Resuelve el siguiente sistema :
\[
\syst{x+y+z=1}{2x-3z=5}{2y+5z=2}
\]
\end{exercice}



\begin{exercice}

Hallar los determinantes : 

\begin{multicols}{2}

\begin{enumerate}[labelindent=\parindent,%
                 leftmargin=*,%
                 label={$\protect {\alph*} = \ $}]



\item $
  \begin{vmatrix}
    2 & 3 &4\\
    -1& -5 & -3\\
    1&4&2
  \end{vmatrix}
$
% 
% \item $
%   \begin{vmatrix}
%     1 & 0 & 2 \\
%     3 & a & 5  \\
%     5 & -a  & 7
%   \end{vmatrix}
% $

\end{enumerate}

 

\end{multicols}



\end{exercice}

\begin{exercice}
Hallar la matriz inversa :
\[
A=\begin{pmatrix} -3&5&6 \\-1&2&2 \\ 1&-1&-1  \end{pmatrix}
\]
\end{exercice}

\vspace{1cm}
\setcounter{exercice}{0}


\devpers{Prueba 2 : sistemas de ecuaciones, determinantes}{}{TS,\ 15 de octubre 2014}{}


\begin{exercice}
 Resuelve el siguiente sistema :
\[
\syst{x+y+z=1}{2x-3z=5}{2y+5z=2}
\]
\end{exercice}



\begin{exercice}

Hallar los determinantes : 

\begin{multicols}{2}

\begin{enumerate}[labelindent=\parindent,%
                 leftmargin=*,%
                 label={$\protect {\alph*} = \ $}]



\item $
  \begin{vmatrix}
    2 & 3 &4\\
    -1& -5 & -3\\
    1&4&2
  \end{vmatrix}
$
% 
% \item $
%   \begin{vmatrix}
%     1 & 0 & 2 \\
%     3 & a & 5  \\
%     5 & -a  & 7
%   \end{vmatrix}
% $

\end{enumerate}

 

\end{multicols}



\end{exercice}

\begin{exercice}
Hallar la matriz inversa :
\[
A=\begin{pmatrix} -3&5&6 \\-1&2&2 \\ 1&-1&-1  \end{pmatrix}
\]
\end{exercice}

\end{document}