Question

Dada a matriz B =(bij) quadrada de ordem 2 com bij= 3i+4j obtenha a transposta dessa matriz

Answer 1

Vamos começar montando a matriz:

$B\;=\;\left[\begin{array}{ccc}b_{_{11}}&b_{_{12}}\\b_{_{21}}&b_{_{22}}\end{array}\right] \\\\\\B\;=\;\left[\begin{array}{ccc}3\,.\,1+4\,.\,1&3\,.\,1+4\,.\,2\\3\,.\,2+4\,.\,1&3\,.\,2+4\,.\,2\end{array}\right]\\\\\\B\;=\;\left[\begin{array}{ccc}7&11\\10&14\end{array}\right]$

Agora podemos determinar a transposta invertendo linha por coluna:

$B^t\;=\;\left[\begin{array}{ccc}7&11\\10&14\end{array}\right]^t\\\\\\B^t\;=\;\left[\begin{array}{ccc}7&10\\11&14\end{array}\right]$