Question

Alguem me ajuda nessa letra b ? Calcular os determinantes

Answer 1

$\left|\begin{array}{cccc}3&- 1&0&0\\2&1&5&4\\3&2&1&0\\- 1&4&- 2&3\end{array}\right| \\ \\ \\ Teorema\: de \: Laplace\: (Cofator) \\ \\ \\ A_i_j = (- 1)^{i + j}\: .\: D_i_J \\ A_1_1 = (- 1)^{1 + 1}\: . \: D_1_1 \\ \\ A_1_1 = 1 . \left|\begin{array}{ccc}1&5&4\\2&1&0\\4&- 2&3\end{array}\right| \\ \\ A_1_1 = \left|\begin{array}{ccc}1 - (5.2)&0 - (4.2)\\- 2- (5.4)&3 - (4.4)\end{array}\right| \\ \\ A_1_1 = \left|\begin{array}{ccc}- 9&- 8\\- 22&- 13\end{array}\right| \\ \\ A_1_1 = 117 - 176 = - 59$

$\left|\begin{array}{cccc}3&- 1&0&0\\2&1&5&4\\3&2&1&0\\- 1&4&- 2&3\end{array}\right| \\ \\ \\ A_1_2 = (-1). \left|\begin{array}{ccc}2&5&4\\3&1&0\\- 1&- 2&3\end{array}\right| \\ \\ A_1_2 = (- 1)(- 59) = 59 \\ \\ \\ det\: B = 3.(- 59) + (- 1).59 \\ det\: B = - 177 - 59 = - 236$