Resposta:

[tex]\textsf{Segue a resposta abaixo}[/tex]

Explicação passo-a-passo:

[tex]\sf M= \left( \begin{array}{ccc}\sf2&\sf4&\sf0\\\sf2&\sf1&\sf4\\\sf-1&\sf-2&\sf0\end{array} \right) [/tex]

[tex]\sf det\,M= \left| \begin{array}{ccc}\sf2&\sf4&\sf0\\\sf2&\sf1&\sf4\\\sf-1&\sf-2&\sf0\end{array}\right|\left|\begin{array}{cc}\sf2&\sf4\\\sf2&\sf1\\\sf-1&\sf-2\end{array}\right|[/tex]

[tex] \mathsf{det\, M= [ 0+(-16)+0]-[0+(-16)+0] }[/tex]

[tex] \mathsf{ det\, M= [-16+0]-[-16+0]}[/tex]

[tex] \mathsf{det\, M=[-16]-[-16] }[/tex]

[tex]\boxed{\boxed{ \mathsf{det\,M=0}} }\leftarrow\textsf{letra C}[/tex]