Question

pfv me ajudem com essa questão

Answer 1

Resposta:

$A^t=\left[\begin{array}{ccc}2&3\\0&2\\1&-3\end{array}\right]$

$A^t\times B=\left[\begin{array}{ccc}8&5&3\\4&-2&2\\-5&7&-3\end{array}\right]$

$Det(A^t.B)=\begin{pmatrix}8&5&3\\ 4&-2&2\\ -5&7&-3\end{pmatrix}\begin{matrix}8&5\\ 4&-2\\ -5&7\end{matrix}$

$Det(A^t.B)=diagonal~~principal - diagonal~~secund\'aria\\ \\ diagonal~~principal:\\ \\ 8.(-2).(-3)+5.(2)(-5)+3.4.7=\\ \\ 48-50+84=132-50=\boxed{82}\\ \\ \\ diagonal~~secund\'aria:\\ \\ (-5)(-2)(3)+7.2.8+(-3).4.5=\\ \\ 30+112-60=142-60=82\\ \\ \\ Det(A^t.B)=82-82=\boxed{0}$