Question

01) Represente em forma de matriz os sistemas abaixo:
a)
x + 3y - 2 = 0
2x + y + z = 1
3x – y +z = 3
b)
2x + y + z = 3
- 2x + 2y – z = 0
3x + y + z = 1
c)
2x + 4y – 2z = 2
- 2x – 2y + 2z = 1
5x + 4y - 3z = 6

Answer 1

Explicação passo-a-passo:

1 3 -2 0

2 1 1 1

3 -1 1 3

D = 1 + 9 + 4 + 6 + 1 - 6

D = 15

0 3 -2

1 1 1

3 -1 1

Dx = 0 + 9 + 2 + 6 + 0 - 3

x = Dx/D = 14/15

1 0 -2

2 1 1

3 3 1

Dy = 1 + 0 - 12 + 6 - 3 + 0

y = Dy/D = -8/15

1 3 0

2 1 1

3 -1 3

Dz = 3 + 9 + 0 + 0 + 1 - 18

z = Dz/D = -1/3

b)

2 1 1 3

-2 2 -1 0

3 1 1 1

D = 4 - 3 - 2 - 6 + 2 + 2

D = -3

3 1 1

0 2 -1

1 1 1

Dx = 6 - 1 + 0 - 2 + 3 + 0

x = Dx/D = -2

2 3 1

-2 0 -1

3 1 1

Dy = 0 - 9 - 2 + 0 + 2 + 6

y = Dy/D = 1

2 1 3

-2 2 0

3 1 1

Dz = 4 + 0 - 6 - 18 + 0 + 2

z = Dz/D = 6

c)

2 4 -2 2

-2 -2 2 1

5 4 -3 6

D = 12 + 40 + 16 - 20 - 16 - 24

D = 8

2 4 -2

1 -2 2

6 4 -3

Dx = 12 + 48 - 8 - 24 - 16 + 12

x = Dx/D = 3

2 2 -2

-2 1 2

5 6 -3

Dy = -6 + 20 + 24 + 10 - 24 - 12

y = Dy/D = 1,5

2 4 2

-2 -2 1

5 4 6

Dz = -24 + 20 - 16 + 20 - 8 + 48

z = Dz/D = 5