Question

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)=

Answer 1

Olá, Jacque.

 

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

 

 

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