1-Considere as matrizes A e B , calcule o pedido e compare os resultados obtidos:A= 1 -2 B= 2 -1 5 -.... Pergunta de ideia deJacque

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1-Considere as matrizes A e B , calcule o pedido e compare os resultados obtidos:

A= 1 -2 B= 2 -1
5 -4 2 3

a- det (A . B) =
b- det (A) . det (B)=

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Olá, Jacque.

$A=\left[\begin{matrix} 1 & -2 \\ 5 & -4 \end{matrix}\right], B=\left[\begin{matrix} 2& -1 \\ 2 & 3 \end{matrix}\right] \\\\\\\\ a)\ det (A \cdot B) = det\left(\left[\begin{matrix} 1\cdot2 -2\cdot2 & 1\cdot(-1)-2\cdot3 \\ 5\cdot 2-4\cdot2 & 5\cdot(-1)-4\cdot3 \end{matrix}\right]\right)=\\\\ =det\left(\left[\begin{matrix} -2 & -7 \\ 2 & -17 \end{matrix}\right]\right) = (-2)\cdot(-17)-2\cdot(-7)=34+14=\boxed{48}$

$b)\ det (A) \cdot det(B) = det\left(\left[\begin{matrix} 1 & -2 \\ 5 & -4 \end{matrix}\right] \right) \cdot det\left(\left[\begin{matrix} 2& -1 \\ 2 & 3 \end{matrix}\right]\right)= \\\\ =[1\cdot(-4)-5\cdot(-2)] \cdot [2\cdot3 - 2\cdot(-1)]=[-4+10]\cdot[6+2]=\\\\=6\cdot8=\boxed{48}$