Question

03. (UESP) Resolva usando a Regra de Cramer. 3x+z=-5 x+y+z=-2 2y-z=-3 03. ( UESP ) Resolva usando a Regra de Cramer . 3x + z = -5 x + y + z = -2 2y - z = -3​

Answer 1

Explicação passo-a-passo:

3x+z=-5

x+y+z=-2

2y-z=-3

3 0 1

1 1 1

0 2 -1

D = 3 . 1 . (-1) + 0 . 1 . 0 + 1 . 1 . 2 - (0 . 1 . 1 + 2 . 1 . 3 + (-1) . 1 . 0)

D = -3 + 0 + 2 + 0 - 6 + 0

D = -7

-5 0 1

-2 1 1

-3 2 -1

Dx = -5 . 1 . (-1) + 0 . 1 . (-3) + 1 . (-2) . 2 - (-3 . 1 . 1 + 2 . 1 . (-5) + (-1) . (-2) . 0)

Dx = 5 + 0 - 4 + 3 + 10 + 0

x = Dx/D

x = 14/(-7)

x = -2

3 -5 1

1 -2 1

0 -3 -1

Dy = 3 . (-2) . (-1) + (-5) . 1 . 0 + 1 . 1 . (-3) - (0 . (-2) . 1 + (-3) . 1 . 3 + (-1) . 1 . (-5))

Dy = 6 + 0 - 3 + 0 + 9 - 5

Dy = 6 + 9 - ( -3 -5 )

Dy = 15-8

Dy = 7

y = Dy/D

y = 7/(-7)

y = -1

3 0 -5

1 1 -2

0 2 -3

Dz = 3 . 1 . (-3) + 0 . (-2) . 0 + (-5) . 1 . 2 - (0 . 1 . (-5) + 2 . (-2) . 3 + (-3) . 1 . 0)

Dz = -9 + 0 - 10 + 0 + 12 + 0

Dz = + 12 - (-9 -10 )

Dz = 12-19

Dz = -7

z = Dz/D

z = -7/(-7)

z = 1