Question

calcule o determinante da matriz( 5 7-2)(-4 0 9) (3 1 -1)​

Answer 1

Regra de Sarrus

$\left[\begin{array}{ccc}5&7&-2\\-4&0&9\\3&1&-1\end{array}\right]$

Adiconando as duas primeiras colunas ao lado da matriz para forma 3 linhas diagonais

Diagonal principal - Diagonal secundária

$\left[\begin{array}{ccc}5&7&-2\\-4&0&9\\3&1&-1\end{array}\right] \[\begin{array}{ccc}5&7\\-4&0\\3&1\end{array}\right]\\\\\\\boxed{5*0*(-1)+7*9*3+(-2)*(-4)*1}-\boxed{30*(-2)-1*9*5-(-1)*(-4)*7}\\\\197-17=180\\\boxed{Det=180}$