Question

Calcule o determinante da matriz

( -2 1 0 )
( 2 3 4 )
( 5 1 2 )

Answer 1

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

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

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

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

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

$\boxed{\boxed{ \mathsf{ det\,A=12}}}$