Question

7 - Ao calcular o determinante, marque a alternativa que
representa corretamente o valor do coeficiente k do
sistema linear:

2x + y - z=0
3y – 2z=0
-2x+5y+kz = 0

A. k= 4
B. k= -3
C. k= -4
D. k= -3
E. k= 2

Answer 1

$\begin{Bmatrix}2x+y-z = 0\\3y-2z = 0\\-2x + 5y + kz = 0\end{matriz} = \left[\begin{array}{ccc}2&1&-1\\0&3&-2\\-2&5&k\end{array}\right] \\\\\\Det :\\\\ 6k + 18 = 0\\6k = -18\\\\\boxed{k = -3}$

Abraços!