Question

Qual a classificacao e a solucao do sistema linar abaixo
x+2y-3z=14
-x+y+z=5
2x+y+5z=18

Answer 1

sistema Possivel ou compativel

Answer 2

Determinante Geral:

$\left|\begin{array}{ccc}1&2&- 3\\- 1&1&1\\2&1&5\end{array}\right|$

$\left|\begin{array}{ccc}1&2&- 3\\- 1&1&1\\2&1&5\end{array}\right| = \left|\begin{array}{ccc}1 - [(2.(-1)]&1 - [(-1)(-3)]\\1 - (2.2)&5 - [(2.(-3)]\end{array}\right| = \left|\begin{array}{ccc}3&- 2\\- 3&11\end{array}\right| = \\ \\ \\ D = 33 - 6 = 27$

D ≠ 0 Logo; SPD

Dx

$\left|\begin{array}{ccc}14&2&- 3\\15&1&1\\18&1&5\end{array}\right|$

$A_i_j = (-1)^{i + j} \: . \: D_i_J \\ \\ A_2_1 = (- 1). \left|\begin{array}{ccc}2& -3\\1&5\end{array}\right| \\ A_2_1 = (-1).13 \\ A_2_1 = - 13 \\ \\ A_2_2 = 1. \left|\begin{array}{ccc}14&- 3\\18&5\end{array}\right| \\ A_2_2 = 124 \\ \\ A_2_3 = (-1). \left|\begin{array}{ccc}14&2\\18&1\end{array}\right| \\ A_2_3 = (-1).(-22) \\ A_2_3 = 22 \\ \\ D_x = 5.(- 13) + 1.124 + 1.22 \\ D_x = -65 + 124 + 22 \\ D_x=81$

Dy

 $\left|\begin{array}{ccc}1&14&- 3\\- 1&5&1\\2&18&5\end{array}\right| = \left|\begin{array}{ccc}19&- 2\\- 10&11\end{array}\right| = 209 - 20 = 189$

Dz

$\left|\begin{array}{ccc}1&2&14\\- 1&1&5\\2&1&18\end{array}\right| = \left|\begin{array}{ccc}3&19\\- 3&- 10\end{array}\right| = - 30 + 57 = 27$

x = Dx/D = 81/27 = 3

y = Dy/D = 189/27 = 7

z = Dz/D = 27/27

S = {(3, 7, 1)}