Question

Verifique se os pontos A (-3, 1), B (0, -3) e C (3, 5) são colineares e calcule o valor do determinante:

Answer 1

O determinante nos dirá se os pontos são colineares.

$D(\left[\begin{array}{ccc}-3&1&1\\0&-3&1\\3&5&1\end{array}\right] )\\0 * (-1)^{i+j} * \left[\begin{array}{cc}1&1\\5&1\end{array}\right] + (-3) * (-1)^{i+j} * \left[\begin{array}{cc}-3&1\\3&1\end{array}\right] + (1) * (-1)^{i+j} * \left[\begin{array}{cc}-3&1\\3&5&\end{array}\right] \\(-3) * (-1)^{2+2} * \left[\begin{array}{cc}-3&1\\3&1\end{array}\right] + (-1)^{2+3} * \left[\begin{array}{cc}-3&1\\3&5&\end{array}\right]$

$(-3) * \left[\begin{array}{cc}-3&1\\3&1\end{array}\right] + (-1) * \left[\begin{array}{cc}-3&1\\3&5&\end{array}\right] \\(-3) * (-3 - 3) + (-1) * (-15 - 3) = (-3)(-6) + (-1)(-18) = 18 + 18 = 36$