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geente,
Resolva o sistema usando a regra de Cramer e calcule x + y + z.
2x - 3y - z = 4
x + 2y + z = 3
3x - y - 2z = 1


RESOLVENDO

Regra de Cramer é um negócio horrível. Nesse caso tu tens que calcular quatro determinantes para encontrar as raízes.
\( D = det \left[\begin{array}{ccc}2&-3&-1\\1&2&1\\3&-1&-2\end{array}\right] => D = -14 \)
\( D_{x} = det \left[\begin{array}{ccc}4&-3&-1\\3&2&1\\1&-1&-2\end{array}\right] => D_{x} = -28 \)
\( D_{y} = det \left[\begin{array}{ccc}2&4&-1\\1&3&1\\3&1&-2\end{array}\right] => D_{y} = 14 \)
\( D_{z} = det \left[\begin{array}{ccc}2&-3&4\\1&2&3\\3&-1&1\end{array}\right] => D_{z} = -42 \)
\( x= \frac{D_{x}}{D} = \frac{-28}{-14} => x=2 \)
\( y= \frac{D_{y}}{D} = \frac{14}{-14} => y=-1 \)
\( z= \frac{D_{z}}{D} = \frac{-42}{-14} => z=3 \)
Por fim, x+y+z=4



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