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\begin{center}
  {\Large Lista de MAT 2116, Primeiro Semestre de 2017}
\end{center}


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\noindent
    {\bf 1)} Sejam $\mathbf{v}_1=(1,0,-1,2)$, $\mathbf{v}_2=(1,1,1,1)$ e $\mathbf{v}_3=(0,1,2,-1)$ e seja $W$ o
    subespa\c{c}o de $\R^4$ gerado por $\{\mathbf{v}_1,\,\mathbf{v}_2,\,\mathbf{v}_3\}$. Encontre uma base de $W$.

   \noindent
       {\bf 2)} Encontre uma base do subespa\c{c}o de $\R^4$ cujos elementos s\ao\ as solu\coes\ $(x,y,z,w)$
       do sistema linear homog\^eneo  ${\displaystyle \left\{\begin{array}{rcl}
         x-z+2w &amp; = &amp; 0\\
         x+y+z+w &amp; = &amp; 0\\
         y+2z+-w &amp; = &amp; 0
         \end{array}\right.}$.

\noindent
    {\bf 3)} Diagonalize 
 ${\displaystyle A=\left[\begin{array}{cccc}
        0 &amp; 0 &amp; 0 &amp; 1  \\
        1 &amp; -1 &amp; 2 &amp; -1  \\
        0 &amp; 0 &amp; 0 &amp; -1  \\
        0 &amp; 0 &amp; 0 &amp; -1  
        \end{array}\right] }$






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