Question

1-Resolva o sistema abaixo utilizando a regra de Cramer.



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Answer 1

Resposta:

x=1, y= -1/2 e z= -1/2

Explicação passo-a-passo:

Regra de Cramer:

$\left[\begin{array}{ccc}1&3&-1\\2&1&1\\3&-1&1\end{array}\right] .\left[\begin{array}{ccc}x\\y\\x\end{array}\right] =\left[\begin{array}{ccc}0\\1\\3\end{array}\right]$

$\Delta=\displaystyle \left[\begin{array}{ccc}1&3&-1\\2&1&1\\3&-1&1\end{array}\right] =(1).(1).(1)+(3).(1).(3)+(2).(-1).(-1)-(3).(1).(-1)-(2).(3).(1)-(-1).(1).(1)=12+(-2)=10$

$\Delta x=\displaystyle \left[\begin{array}{ccc}0&3&-1\\1&1&1\\3&-1&1\end{array}\right] =(0).(1).(1)+(3).(1).(3)+(1).(-1).(-1)-(3).(1).(-1)-(1).(3).(1)-(-1).(1).(0)=10+(0)=10$

$\Delta y=\displaystyle \left[\begin{array}{ccc}1&0&-1\\2&1&1\\3&3&1\end{array}\right] =(1).(1).(1)+(0).(1).(3)+(2).(3).(-1)-(3).(1).(-1)-(2).(0).(1)-(3).(1).(1)=-5+(0)=-5$

$\Delta z=\displaystyle \left[\begin{array}{ccc}1&3&0\\2&1&1\\3&-1&3\end{array}\right] =(1).(1).(3)+(3).(1).(3)+(2).(-1).(0)-(3).(1).(0)-(2).(3).(3)-(-1).(1).(1)=12+(-17)=-5$

x=Δx/Δ=10/10=1

y=Δy/Δ= -5/10= -1/2

z=Δz/Δ= -5/10= -1/2