Question

$<var>A=\left[\begin{array}{ccc}1&5&-3\\-1&7&0\\2&4&9\end{array}\right]</var>$

Answer 1

Como você pediu no chat ;)

Resolverei por laplace.

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

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

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

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

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

$det(A)=63+57+42$

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