Question

Resolva o sistema { 2x - 2y -4y = 2 {-x + y + z = 2 {X -2y + z = -2 Alternativa que mostra os valores de x, y e Z.

Answer 1

2x - 2y -4z = 2 (:2)

-x + y + z = 2

X -2y + z = -2

x - y - 2z = 1

- x + y + z = 2

x - 2y + z = - 2

[1 -1 -2 1 -1]

[-1 1 1 -1 1]

[1 - 2 1 1 - 2]

D = 1 - 1 - 4 - ( - 2 - 2 + 1)

D = 0 - 4 - ( - 4 + 1)

D = - 4 - ( - 3)

D = - 4 + 3

D = - 1

[ 1 -1 -2 1 -1]

[ 2 1 1 2 1]

[-2 -2 1 -2 -2]

Dx = 1 + 2 + 8 - (4 - 2 - 2)

DX = 11 - (0)

DX = 11

X = DX/d = 11/(-1) = - 11

[ 1 1 -2 1 1]

[-1 2 1 -1 2]

[1 -2 1 1 -2]

Dy = 2 + 1 - 4 - (- 4 - 2 - 1)

Dy = - 1 - ( - 7)

Dy = - 1 + 7

Dy = 6

Y = dy/d = 6/(-1) = - 6

[ 1 -1 1 1 -1]

[-1 1 2 -1 1]

[ 1 -2 -2 1 -2]

Dz = - 2 - 2 + 2 - [ 1 - 4 - 2]

Dz = - 4 + 2 - ( 1 - 6)

Dz = - 2 - (-5)

Dz = - 2 + 5

Dz = 3

Z = dz/d = 3/(-1) = - 3

R.:

X = - 11; y = - 6; z = - 3