Question

Calcule o determinantes das matrizes

Answer 1

$\left|\begin{array}{ccc}2&3&4\\5&- 1&3\\2&7&4\end{array}\right| \\ \\ \\ A_i_j = (- 1)^{i + j}\:.\: D_i_j \\ A_1_1 = (- 1)^{1 + 1}\:.\: D_1_1 \\ \\ A_1_1 = 1 . \left|\begin{array}{ccc}- 1&3\\7&4\end{array}\right| = - 25 \\ \\ A _1_2 = (- 1). \left|\begin{array}{ccc}5&3\\2&4\end{array}\right| = (- 1).14 = - 14 \\ \\ A_1_3 = 1. \left|\begin{array}{ccc}5&- 1\\2&7\end{array}\right| = 37 \\ \\ \\ det\: A = (- 25).2 + (- 14).3 + 37.4 \\ det\: A = - 50 - 42 + 178 = 86$

$\left|\begin{array}{ccc}sen\: x &cos\: x\\cos\: x&sen\: x\end{array}\right| = (sen\: x.sen\: x) - (cos\: x.cos\: x) = sen^2\: x - cos^2\: x$

Regra De Chió 

$\left|\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right| = \left|\begin{array}{ccc}5 - (4.2)&6 - (4.3)\\8 - (7.2)&9 - (7.3)\end{array}\right| = \left|\begin{array}{ccc}- 3&- 6\\- 6&12\end{array}\right| = - 36 + 36 = 0$

$\left|\begin{array}{ccc}2&3\\1&4\end{array}\right| = 8 - 3 = 5$

5 + 0 = 5

Resolva as proximas alternativas