Question

Calcule o determinante da matriz a seguir:​

Answer 1

Utilizando a regra de Sarrus, temos:

$Repetimos~ as~ duas~ primeiras~ linha ~e ~fazemos ~as~ multiplicacoes~(diagonais)\\\\\left|\begin{array}{ccc}-1&3&1\\4&1&10\\-2&2&0\\-1&3&1\\4&1&10\end{array}\right|~=\\\\\\=~(~(-1).1.0~+~4.2.1~+~(-2).3.10~)~-~(~1.1.(-2)~+~10.2.(-1)~+~0.3.4~)\\\\\\=~(~0~+~8~+~(-60)~)~-~(~(-2)~+~(-20)~+~0~)\\\\\\=~(~-52~)~-~(~-22~)\\\\\\=~-52+22\\\\\\=~\boxed{-30}$