Question

O conjunto verdade do sistema (alguem pode me ajudar)

Answer 1

 Resolver pela regra de Cramer

$D= \left[\begin{array}{ccccc}1&2&-1&1&2\\3&-4&5&3&4\\1&1&1&1&1\end{array}\right] \\ \\ D=-4+10-3-(4+5+6) \\ D=-4+10-3-4-5-6 \\ D=-22+10 \\ D=-12$ 


$D_X= \left[\begin{array}{ccccc}0&2&-1&0&2\\10&-4&5&10&-4\\1&1&1&1&1\end{array}\right] \\ \\ \\ D_X=0+10-10-(4+0+20) \\ D_X=10-10-4-20 \\ D_X=-34+10 \\ D_X=-24$ 


$D_Y= \left[\begin{array}{ccccc}1&0&-1&1&0\\3&10&5&3&10\\1&1&1&1&1\end{array}\right] \\ \\ \\ D_Y=10+0-3-(-10+5+0) \\ D_Y=10-3+10-5 \\ D_Y=20-8 \\ D_Y=12$ 


$D_Z= \left[\begin{array}{ccccc}1&2&0&1&2\\3&-4&10&3&-4\\1&1&1&1&1\end{array}\right] \\ \\ \\ D_Z=-4+20+0-(0+10+6) \\ D_Z=-4+20-10-6 \\ D_Z=-20+20 \\ D_Z=0$ 

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vamos calcular x,y,z

$x= \frac{D_X}{D} = \frac{-24}{-12} =2 \\ \\ y= \frac{D_Y}{D} = \frac{12}{12} =1 \\ \\ z= \frac{D_Z}{D} = \frac{0}{-12} =0 \\ \\ S=\{(2,-1,0)\}~~~~letra~~C$