Question

Calcule o determinante da matriz M= |1 1 -1| usando o Teorema de La
|1 -1 -2| Place
|1 2 1|

Answer 1

$\left|\begin{array}{ccc}1&1&- 1\\1&- 1&- 2\\1&2&1\end{array}\right| \\ \\ \\ A_i_j = (- 1)^{i + j} \: . \: D_i_j \\ A_1_1 = (- 1)^{1 + 1}\: . \: D_1_1 \\ \\ A_1_1 = 1. \left|\begin{array}{ccc}- 1&- 2\\2&1\end{array}\right| \\ \\ A_1_1 = 3 \\ \\ A_1_2 = (- 1). \left|\begin{array}{ccc}1&- 2\\1&1\end{array}\right| \\ \\ A_1_2 = (- 1).3 = - 3 \\ \\ A_1_3 = 1. \left|\begin{array}{ccc}1&- 1\\1&2\end{array}\right| \\ \\ A_1_3 = 3 \\ \\ det\: A = 1.3 + 1.(- 3) + (- 1).3 \\ det\: A = 3 - 3 + 3 = 3$