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\begin{document}

\begin{figure}[!htb]
\centering
\includegraphics[scale=0.4]{logoNH.ps}
\end{figure}

\vspace{2cm}


\begin{exercise}
Sendo $A=\left(
        \begin{array}{cc}
          3 & -1 \\
          4 & 0 \\
        \end{array}
      \right)$ e $B=\left(
                    \begin{array}{cc}
                      -1 & 7 \\
                      -2 & 4 \\
                    \end{array}
                  \right)$, encontre o valor da matriz X, para que se tenha
                  $\frac{X-A}{2}=\frac{X+2B}{3}$.
\end{exercise}

\vspace{2cm}



\begin{exercise}
Sendo $A$ uma matriz $3$ por $3$, definida pela lei
$a_{ij}=\begin{cases}
1, & \text{se $i=j$},\\
i^2, & \text{se $i\neq j$}.
\end{cases}$

Responda:
\begin{description}
\item[(a)] Determine a mattriz A;
\item[(b)] Encontre o traço desta matriz;
\item[(c)] Encontre o determinante desta matriz;
\item[(d)] Encontre a inversa desta matriz, se existir.
\end{description}
\end{exercise}

\vspace{2cm}


\begin{exercise}
Se $\left(
     \begin{array}{cc}
       2 & 3 \\
       1 & 4 \\
     \end{array}
   \right)$ $\left(
              \begin{array}{cc}
                a & 1 \\
                -2 & b \\
              \end{array}
            \right)$ = $\left(
                         \begin{array}{cc}
                           5 & 7 \\
                           -5 & 9 \\
                         \end{array}
                       \right)$, calcule o valor de $a+b$.
\end{exercise}

\vspace{2cm}

\begin{exercise}
Dadas as matrizes $A=\left(
                       \begin{array}{cc}
                         2 & 0 \\
                         -1 & 3 \\
                       \end{array}
                     \right)$ e $B=\left(
                                     \begin{array}{cc}
                                       2 & \frac{1}{2} \\
                                       4 & 3 \\
                                     \end{array}
                                   \right)$, encontre o valor de
                                   $-3BA$.
\end{exercise}


\vspace{1cm}

\emph{"Eu voltei pra minha sina, contei  pra uma menina, meu medo só
termina estando ali, ela é suave assim, e sabe quase tudo de mim,
ela sabe onde eu, queria estar enfim. É tanto, é tanto. Se ao menos
você soubesse. Te quero tanto."} - Tanto (I Want You) (Bob Dylan).



\end{document}