Question

1) Dada as matrizes abaixo,o determinante da matriz A•B é A= [1 3 24] [-1 2 3 1 ]​

Answer 1

$\textrm{Sejam\ as\ matrizes}\ A\ \textrm{e}\ B\ \textrm{dadas por:}$

$A=\left[\begin{array}{cc}1&3\\2&4\end{array}\right]\ \text{e}\ B=\left[\begin{array}{cc}-1&2\\3&1\end{array}\right]$

$\mathrm{O\ determinante\ da\ matriz}\ AB\ \mathrm{ser\acute{a}}\text{:}$

$\boxed{\det{AB}=\det{A}\det{B}}$

$\Longrightarrow \det{AB}=\left|\begin{array}{cc}1&3\\2&4\end{array}\right|\left|\begin{array}{cc}-1&2\\3&1\end{array}\right|$

$\Longrightarrow \det{AB}=\left(4-6\right)\left(-1-6\right)$

$\Longrightarrow \det{AB}=\left(-2\right)\left(-7\right)\ \therefore\ \boxed{\det{AB}=14}$