Question

Encontre o determinante da matriz A = (aij )³×³, tal que aij = 4+i-2j.​

Answer 1

Resposta: o valor do determinante da matriz A = 0.

Resolução:

Matriz:

$A=\left[\begin{array}{ccc}4+1-2.1&4+1-2.2&4+1-2.3\\4+2-2.1&4+2-2.2&4+2-2.3\\4+3-2.1&4+3-2.2&4+3-2.3\end{array}\right] \\\\\\A=\left[\begin{array}{ccc}5-2&5-4&5-6\\6-2&6-4&6-6\\7-2&7-4&7-6\end{array}\right] \\\\\\A=\left[\begin{array}{ccc}3&1&-1\\4&2&0\\5&3&1\end{array}\right]$

Cálculo do determinante pela Regra de Sarrus:

$Det(A) = [3.2.1 +1.0.5+(-1).4.3] - [(-1).2.5+3.0.3+1.4.1]\\Det(A) = [6 + 0 - 12] -[-10+0+4]\\Det(A) = [-6] - [-6]\\Det(A) = -6 + 6\\Det(A) = 0$