Question

resolución por el método cramer 3x-5y+8z = 17 x+y+z=6 2x+y=z=1​

Answer 1

Respuesta:

(x,y,z)= (-5,56/13,87/13)

Answer 2

Respuesta:

x=1

y=2

z=3

Explicación paso a paso:

$Det=\left[\begin{array}{ccc}3&-5&8\\1&1&1\\2&1&-1\end{array}\right] =(3)(1)(-1)+(1)(1)(8)+(2)(-5)(1)-(2)(1)(8)-(1)(1)(3)-(-1)(1)(-5)=-29$

$Detx=\left[\begin{array}{ccc}17&-5&8\\6&1&1\\1&1&-1\end{array}\right] =(17)(1)(1)+(6)(1)(8)+(1)(-5)(1)-(1)(1)(8)-(1)(1)(17)-(-1)(6)(-5)=-29\\\\Dety=\left[\begin{array}{ccc}3&17&8\\1&6&1\\2&1&-1\end{array}\right] =(3)(6)(-1)+(1)(1)(8)+(2)(17)(1)-(2)(6)(8)-(1)(1)(3)-(-1)(1)(17)=-58\\\\Detz=\left[\begin{array}{ccc}3&-5&17\\1&1&6\\2&1&1\end{array}\right] =(3)(1)(1)+(1)(1)(17)+(2)(-5)(6)-(2)(1)(17)-(1)(6)(3)-(1)(1)(-5)=-87$

Entonces las soluciones son:

$x=\frac{Detx}{Det}=\frac{-29}{-29}=1 \\y=\frac{Dety}{Det}=\frac{-58}{-29}=2\\z=\frac{Detz}{Det}=\frac{-87}{-29}=3$