Question

calcule a determinante
$\left[\begin{array}{ccc}1&3&5\\2&4&6\\-4&1&-1\end{array}\right]$

Answer 1

Utilizando a regra de Sarrus, temos:

$\left|\begin{array}{ccc}1&3&5\\2&4&6\\-4&1&-1\\1&3&5\\2&4&6\end{array}\right|~=\\\\\\\\=~\left(~1.4.(-1)+2.1.5+(-4).3.6~\right)~-~\left(~5.4.(-4)+6.1.1+(-1).3.2~\right)\\\\\\=~\left(~-4+10-72~\right)~-~\left(~-80+6-6~\right)\\\\\\=~\left(~-66~\right)~-~\left(~-80~\right)\\\\\\=~-66+80\\\\\\=~\boxed{14}$