Question

Qual é o determinante da matriz abaixo:

$\begin{array}{ | c c c c c| } 0& - 1&0&1 &0 \\ 2&0& - 3&2&1 \\ 1&2&0&3&0 \\ 1&0&0&0&0 \\ - 3&0&0&0&2\end{array}$
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Answer 1

$\begin{array}{ | c c c c c| } 0& - 1&\diagup\!\!\!\!0&1 &0 \\ \diagup\!\!\!\! 2&\diagup\!\!\!\! 0& - \diagup\!\!\!\! 3&\diagup\!\!\!\!2&\diagup\!\!\!\!1 \\ 1&2&\diagup\!\!\!\!0&3&0 \\ 1&0&\diagup\!\!\!\!0&0&0 \\ - 3&0&\diagup\!\!\!\!0&0&2\end{array}\Rightarrow\begin{array}{ | c c c c | }\diagup\!\!\!\!0 & - 1&1&0 \\ \diagup\!\!\!1&2&3&0 \\ \diagup\!\!\!\!1&\diagup\!\!\!\!0&\diagup\!\!\!\!0&\diagup\!\!\!\!0 \\ -\diagup\!\!\!\! 3&0&0&2\end{array}\Rightarrow$

$\begin{array}{ | c c c | } - 1&1& \diagup\!\!\!\!0 \\ 2& 3& \diagup\!\!\!\!0 \\ \diagup\!\!\!\!0& \diagup\!\!\!\!0& \diagup\!\!\!\!2 \end{array}\Rightarrow\begin{array}{ | c c | } - 1& 1 \\ 2& 3\end{array} = - 1 \cdot3 - 1 \cdot2 = - 5$

$\Delta = 3 \cdot1 \cdot2 \cdot( - 5)\Rightarrow \boxed{ \boxed{\Delta = - 30}}$