Question

Resolva por favor
x + 3y + 5z + 7w = 12
3x + 5y + 7z + w = 0
5x + 7y + z + 3w = 4
7x + y + 3z + 5w = 16

Answer 1

Vamos là.

x + 3y + 5z + 7w = 12

3x + 5y + 7z + w = 0

5x + 7y + z + 3w = 4

7x + y + 3z + 5w = 16

4x + 8y + 12z + 8w = 12

12x + 8y + 4z + 8w = 20

8x - 8z = 8

x = z + 1

4x = 4z + 4

4z + 4 + 8y + 12z + 8w = 12

8y + 16z + 8w = 8

y + 2z + w = 1

5x = 5z + 5

5z + 5 + 7y + z + 3w = 4

7y + 6z + 3w = -1

y + 2z + w = 1

3y + 6z + 3w = 3

4y = -4

y = -1

x = z  + 1

z + 1 - 3 + 5z + 7w = 12

6z + 7w = 14

3z + 3 - 5 + 7z + w = 0

10z + w = 2

70z + 7w = 14

z = 0

w = 2

x = z + 1 = 1

S = (1, -1, 0, 2)