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  • Usuário do Brainly
2014-05-05T23:34:21-03:00
Como você pediu no chat ;)

Resolverei por laplace.

A=\begin{bmatrix}1&5&-3\\-1&7&0\\2&4&9\end{bmatrix}

det(A)=(-1)^{1+1}*a_{1,1}*\begin{vmatrix}7&0\\4&9\end{vmatrix}+(-1)^{1+2}*a_{2,1}*\begin{vmatrix}5&-3\\4&9\end{vmatrix}+\\(-1)^{1+3}*a_{3,1}*\begin{vmatrix}5&-3\\7&0\end{vmatrix}

det(A)=a_{1,1}*\begin{vmatrix}7&0\\4&9\end{vmatrix}-a_{2,1}*\begin{vmatrix}5&-3\\4&9\end{vmatrix}+a_{3,1}*\begin{vmatrix}5&-3\\7&0\end{vmatrix}

det(A)=\begin{vmatrix}7&0\\4&9\end{vmatrix}+\begin{vmatrix}5&-3\\4&9\end{vmatrix}+2*\begin{vmatrix}5&-3\\7&0\end{vmatrix}

det(A)=63+57+2*21

det(A)=63+57+42

\boxed{\boxed{det(A)=162}}
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