Question

resolva pela regra de cramer
x+y+z=6
-x+y+3z=10
5x+y-z=4​

Answer 1

Resposta:

x = 1, y = 2 e z = 3

Explicação passo-a-passo:

x+y+z=6

-x+y+3z=10

5x+y-z=4

Primeiro você deve calcular o determinante da matriz incompleta:

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

Calculando o det pela regra de Sarrus

Det = -1 + 15 - 1 - 5 - 3 - 1

Det = 15 - 11

Det = 4

Calculando o det de x:

$\left[\begin{array}{ccc}6&y&z\\10&y&z\\4&y&z\end{array}\right] = \left[\begin{array}{ccc}6&1&1\\10&1&3\\4&1&-1\end{array}\right]$

Detx = 4

Calculando o det de y:

$\left[\begin{array}{ccc}x&6&z\\x&10&z\\x&4&z\end{array}\right] = \left[\begin{array}{ccc}1&6&1\\-1&10&3\\5&4&-1\end{array}\right]$

Dety = 8

Calculando o det z:

$\left[\begin{array}{ccc}x&y&6\\x&y&10\\x&y&4\end{array}\right] = \left[\begin{array}{ccc}1&1&6\\-1&1&10\\5&1&4\end{array}\right]$

Detz = 12

Calculando x, y e z:

$x = \frac{Detx}{Det} = \frac{4}{4} = 1 \\x = 1$

$y = \frac{Dety}{Det} = \frac{8}{4} = 2\\y = 2$

$z = \frac{Detz}{Det} = \frac{12}{4} = 3$