Question

Resolva os intes abaixo, utilizando regra de cramer:

| x + y = 4
| y - z = 10
| 3x + z = -4

Calcule o Determinante D :

Dx :

Dy :

Dz :​

Answer 1

{ 1.x +1.y +0.z = 4

{ 0.x +1.y -1.z = 10

{ 3.x +0.y +1.z = -4

$D=\left|\begin{array}{ccc}1&1&0\\0&1&-1\\3&0&1\end{array}\right| \\\\1.1.1+1.(-1).3+0.0.0-[0.1.3+1.0.(-1)+1.1.0]\\1-3\\-2$

 Para descobrir Dx, substituiremos a linha do x pela linha dos termos sem incógnita, mesma coisa com Dy e Dz:

$D_x=\left|\begin{array}{ccc}4&1&0\\10&1&-1\\-4&0&1\end{array}\right| \\\\4.1.1+10.0.0+1.(-1).(-4)-[0.1.(-4)+4.0.(-1)+10.1.1]\\4+4-[10]\\8-10\\-2$

$D_y=\left|\begin{array}{ccc}1&4&0\\0&10&-1\\3&-4&1\end{array}\right| \\\\\\1.10.1+4.3.(-1)+0.(-4).0-[0.10.3+1.(-4).(-1)+0.4.1]\\10-12-[4]\\-2-4\\-6$

$D_z=\left|\begin{array}{ccc}1&1&4\\0&1&10\\3&0&-4\end{array}\right| \\\\1.1.(-4)+4.0.0+10.1.3-[4.1.3+1.10.0+1.0.(-4)]\\-4+30-[12]\\26-12\\14$

 Agora para encontrar os valores de x, y e z:

$x=\frac{D_x}{D}\\x=\frac{-2}{-2}\\x=1\\\\y=\frac{D_y}{D}\\y=\frac{-6}{-2}\\y=3\\\\z=\frac{D_z}{D}\\z=\frac{14}{-2}\\z = -7$

Dúvidas só perguntar!