Question

O determinante da matriz A

(-2 1 0

2 3 4

5 1 2)
é igual a:


a. det (A) = -4

b. det (A) = 4

c. det (A) = 12

d. det (A) = -12

e. det (A) = 8

Answer 1

Resposta:

$\textsf{Segue a resposta abaixo}$

Explicação passo-a-passo:

$\begin{gathered}\sf A=\left(\begin{array}{ccc}\sf-2&\sf1&\sf0\\\sf2&\sf3&\sf4\\\sf5&\sf1&\sf2\end{array}\right)\end{gathered}$

$\begin{gathered}\left|\begin{array}{ccc}\sf-2&\sf1&\sf0\\\sf2&\sf3&\sf4\\\sf5&\sf1&\sf2\end{array}\right|\left|\begin{array}{cc}\sf-2&\sf1\\\sf2&\sf3\\\sf5&\sf1\end{array}\right|\end{gathered}$

$\mathsf{ det\,(A)=[-12+20+0]-[4+(-8)+0]}$

$\mathsf{ det\,(A)=[8+0]-[-4+0]}$

$\mathsf{ det\,(A)=[8]-[-4]}$

$\boxed{\boxed{ \mathsf{ det\,(A)=12}}}\leftarrow\textsf{letra C}$