Question

1) Resolva os Sistemas abaixo utilizando a Regra de Cramer:
a)
3x - y + z = 1
2x + 3z = -1
4x + y - 2z=7

b) x - y + z = -5
x + 2y + 4z = 4
3x + y - 2z=-3​

Answer 1

Explicação passo-a-passo:

a)

3 -1 1

2 0 3

4 1 -2

D = 0 - 12 + 2 + 0 - 9 - 4

D = -23

1 -1 1

-1 0 3

7 1 -2

Dx = 0 - 21 - 1 + 0 - 3 + 2

x = Dx/D

x = -23/(-23)

x = 1

3 1 1

2 -1 3

4 7 -2

Dy = 6 + 12 + 14 + 4 - 63 + 4

Dz = 6 + 12 + 14 + 4 + 4 - ( -63 )

Dz = 40-63

Dz = -23

y = Dy/D

y = -23/(-23)

y = 1

3 -1 1

2 0 -1

4 1 7

Dz = 0 + 4 + 2 + 0 + 3 + 14

Dz = + 4 + 2 + 3 + 14 - ( )

Dz = 230

Dz = 23

z = Dz/D

z = 23/(-23)

z = -1

b)

1 -1 1

1 2 4

3 1 -2

D = -4 - 12 + 1 - 6 - 4 - 2

D = -27

-5 -1 1

4 2 4

-3 1 -2

Dx = 20 + 12 + 4 + 6 + 20 - 8

x = Dx/D

x = 54/(-27)

x = -2

1 -5 1

1 4 4

3 -3 -2

Dy = -8 - 60 - 3 - 12 + 12 - 10

Dz = + 12 - (-8 -60 -3 -12 -10 )

Dz = 12-93

Dz = -81

y = Dy/D

y = -81/(-27)

y = 3

1 -1 -5

1 2 4

3 1 -3

Dz = -6 - 12 - 5 + 30 - 4 - 3

Dz = + 30 - (-6 -12 -5 -4 -3 )

Dz = 30-30

Dz = 0

z = Dz/D

z = 0/(-27)

z = 0