Resposta:
a) A (-2, 5), B (3,7) e C (5,11)
[tex]\left[\begin{array}{ccc}-2&5&1\\3&7&1\\5&11&1\end{array}\right] = 0\\\\\left[\begin{array}{ccc}-2&5&1\\3&7&1\\5&11&1\end{array}\right] = \left[\begin{array}{ccc}-2&5\\3&7\\5&11\end{array}\right][/tex]
-2 . 7 . 1 = -14 1 . 7 . 5 = 35
5 . 1 . 5 = 25 -2 . 1 . 11 = -22
1 . 3 . 11 = 33 5 . 3 . 1 = 15
(-14 + 25 + 33) - (35 - 22 +15)
44 - 28 = 16 Não está alinhado
b) A (0, 4), B (-6,2) e C (8,10)
[tex]\left[\begin{array}{ccc}0&4&1\\-6&2&1\\8&10&1\end{array}\right] = 0\\\\\left[\begin{array}{ccc}0&4&1\\-6&2&1\\8&10&1\end{array}\right] = \left[\begin{array}{ccc}0&4\\-6&2\\8&10\end{array}\right][/tex]
0 . 2 . 1 = 0 1 . 2 . 8 = 16
4 . 1 . 8 = 32 0 . 1 . 10 = 0
1 . -6 . 10 = - 60 4 . -6 . 1 = - 24
(0 + 32 - 60) - (16 + 0 - 24)
- 28 - (- 8) = -28 + 8 = -20 Não está alinhado
c) A (1,5), B ( 3,4) e C (2,2)
[tex]\left[\begin{array}{ccc}1&5&1\\3&4&1\\2&2&1\end{array}\right] = 0\\\\\left[\begin{array}{ccc}1&5&1\\3&4&1\\2&2&1\end{array}\right] = \left[\begin{array}{ccc}1&5\\3&4\\2&2\end{array}\right][/tex]
1 . 4 . 1 = 4 1 . 4 . 2 = 8
5 . 1 . 2 = 10 1 . 1 . 2 = 2
1 . 3 . 2 = 6 5 . 3 . 1 = 15
(4 + 10 + 6) - (8 + 2 + 15)
20 - 25 = - 5 Não está alinhado.
d) A (-4, -3), B (-1, 1) e C (2, 5)
[tex]\left[\begin{array}{ccc}-4&-3&1\\-1&1&1\\2&5&1\end{array}\right] = 0\\\\\left[\begin{array}{ccc}-4&-3&1\\-1&1&1\\2&5&1\end{array}\right] = \left[\begin{array}{ccc}-4&-3\\-1&1\\2&5\end{array}\right][/tex]
-4 . 1 . 1 = - 4 1 . 1 . 2 = 2
- 3 . 1 . 2 = - 6 - 4 . 1 . 5 = - 20
1 . - 1 . 5 = - 5 - 3 . - 1 . 1 = 3
(- 4 - 6 - 5) - ( 2 - 20 + 3)
- 15 - (- 15)
- 15 + 15 = 0 Está alinhado
e) A (-1,02), B (1, 3) e C (2, 5)
[tex]\left[\begin{array}{ccc}-1&2&1\\1&1&3\\3&4&1\end{array}\right] = 0\\\\\left[\begin{array}{ccc}-1&2&1\\1&1&3\\3&4&1\end{array}\right] = \left[\begin{array}{ccc}-1&2\\1&3\\3&4\end{array}\right][/tex]
-1 . 1 . 1 = -1 1 . 1 . 3 = 3
2 . 3 . 3 = 18 -1 . 3 . 4 = - 12
1 . 1 . 4 = 4 2 . 1 . 1 = 2
(-1 + 18 + 4) - ( 3 - 12 + 2)
31 - (- 7) = 31 + 7 = 38 Não esta equilibrado
