Question

Qual o valor do determinante da matriz A -
[-1 3 1]
[4 1 10]
[-2 2 0]​

Answer 1

Explicação passo-a-passo:

Temos a seguinte matriz A:

$A=\left[\begin{array}{ccc}-1&3&1\\4&1&10\\-2&2&0\end{array}\right]$

Calculando o determinante:

$detA=\left|\begin{array}{ccc}-1&3&1\\4&1&10\\-2&2&0\end{array}\right|\\\\\text Usando\ a\ Regra\ de\ Sarrus:\\\\detA=\left|\begin{array}{ccc}-1&3&1\\4&1&10\\-2&2&0\end{array}\right\left|\begin{array}{ccc}-1&3\\4&1\\-2&2\end{array}\right|\\\\detA=(-1).1.0+3.10.(-2)+1.4.2-3.4.0-(-1).10.2-1.1.(-2)\\\\detA=0-60+8-0+20+2\\\\\boxed{\boxed{detA=-30}}$

Resposta D