Question

Por favor, Dadas as matrizes​

Answer 1

Vamos começar determinando a transposta de N.

Para isso, as linhas de N viram colunas na transposta e as colunas de N viram linhas na transposta.

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

Agora sim, podemos calcular o produto de M pela transposta de N:

$M~.~N^t~=~\left[\begin{array}{ccc}-4&1\\3&2\end{array}\right]~.~\left[\begin{array}{ccc}2&1\\0&-2\end{array}\right]\\\\\\M~.~N^t~=~\left[\begin{array}{ccc}(-4)\,.\,2~+~1\,.\,0&(-4)\,.\,1~+~1\,.\,(-2)\\3\,.\,2~+~2\,.\,0&3\,.\,1~+~2\,.\,(-2)\end{array}\right]\\\\\\M~.~N^t~=~\left[\begin{array}{ccc}-8~+~0&-4~-~2\\6~+~0&3~-~4\end{array}\right]\\\\\\M~.~N^t~=~\left[\begin{array}{ccc}-8&-6\\6&-1\end{array}\right]$