Question

Sendo A = (
1 2
3 4
) e B = (
2 0
1 2
), mostre que:

Answer 1

$a) A^{t}= \left[\begin{array}{ccc}1&3\\2&4\end{array}\right] ; (A^{t})^{t} = \left[\begin{array}{ccc}1&2\\3&4\end{array}\right] =A ; \\ \\ b)(A+B) = \left[\begin{array}{ccc}3&2\\4&6\end{array}\right] \\ \\ (A+B)^{t} = \left[\begin{array}{ccc}3&4\\2&6\end{array}\right] ~e~A^{t} +B^{t} = \left[\begin{array}{ccc}1&3\\2&4\end{array}\right] + \left[\begin{array}{ccc}2&1\\0&2\end{array}\right] = \left[\begin{array}{ccc}3&4\\2&6\end{array}\right]$ $c)2A= \left[\begin{array}{ccc}2&4\\6&8\end{array}\right] ;(2A)^{t} = \left[\begin{array}{ccc}2&6\\4&8\end{array}\right] ;A^{t} = \left[\begin{array}{ccc}1&3\\2&4\end{array}\right] ~e~2A ^{t}= \left[\begin{array}{ccc}2&6\\4&8\end{array}\right]$