Question

Resolva o sistema a seguir por Regra de Cramer ou Escalonamento: 2x + y − 8z = −5
x + y − 2z = 0
{
x + 2y + 3z = 6

Answer 1

Resposta:

x=y=z=1

Explicação passo-a-passo:

Regra de Cramer

$\left[\begin{array}{ccc}2&1&-8\\1&1&-2\\1&2&3\end{array}\right] .\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-5\\0\\6\end{array}\right]$

$\Delta =\displaystyle \left[\begin{array}{ccc}2&1&-8\\1&1&-2\\1&2&3\end{array}\right] =(2).(1).(3)+(1).(-2).(1)+(1).(2).(-8)-(1).(1).(-8)-(1).(1).(3)-(2).(-2).(2)=-12+(13)=1$

$\Delta x=\displaystyle \left[\begin{array}{ccc}-5&1&-8\\0&1&-2\\6&2&3\end{array}\right] =(-5).(1).(3)+(1).(-2).(6)+(0).(2).(-8)-(6).(1).(-8)-(0).(1).(3)-(2).(-2).(-5)=-27+(28)=1$

$\Delta y=\displaystyle \left[\begin{array}{ccc}2&-5&-8\\1&0&-2\\1&6&3\end{array}\right] =(2).(0).(3)+(-5).(-2).(1)+(1).(6).(-8)-(1).(0).(-8)-(1).(-5).(3)-(6).(-2).(2)=-38+(39)=1$

$\Delta z=\displaystyle \left[\begin{array}{ccc}2&1&-5\\1&1&0\\1&2&6\end{array}\right] =(2).(1).(6)+(1).(0).(1)+(1).(2).(-5)-(1).(1).(-5)-(1).(1).(6)-(2).(0).(2)=2+(-1)=1$

x=Δx/Δ=1/1=1

y=Δy/Δ=1/1=1

z=Δz/z=1/1=1