Question

Resolvendo o sistema de equações lineares
3x - y + 2z = 7
2x - 3y + z = -1
x + 2y - z = 2


encontramos y igual a
A) 1 B) 3 C) 5 D) 2 E) 4
Gabarito: d) 2

Answer 1

usando o metodo de cramer:

$D = \left[\begin{array}{ccc}3&-1&2\\2&-3&1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}3&-1&\\2&-3&\\1&2&\end{array}\right] D = 3*-3*-1-1*1*1+2*2*2-2*-3*1-3*1*2+1*2*-1 = 14$$Dy = \left[\begin{array}{ccc}3&7&2\\2&-1&1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}3&7&\\2&-1&\\1&2&\end{array}\right] Dy = 3*-1*-1+7*1*1+2*2*2-2*-1*1-3*1*2-7*2*-1 = 28 y = Dy/D = 28/14 = 2$