Question

Determine -2A
3A+6B
4At-3Bt

Answer 1

$A = (-2) \left[\begin{array}{ccc}4&9\\-7&2\end{array}\right] = \left[\begin{array}{ccc}-8&-18\\14&-4\end{array}\right]_2 \\ \\ \\ 3A + 6B \\ \\ 3 \left[\begin{array}{ccc}4&9\\-7&2\end{array}\right] + 6 \left[\begin{array}{ccc}-1&0\\3&-4\end{array}\right] \\ \\ \left[\begin{array}{ccc}12&27\\-21&6\end{array}\right] + \left[\begin{array}{ccc}-6&0\\18&-24\end{array}\right] = \left[\begin{array}{ccc}6&27\\-3&-18\end{array}\right]_2$

Matriz Transposta: ( aij = aji ) Inverte - se (i linhas para j colunas ou j colunas para i linhas)

$4A^t - 3B^t \\ \\ 4 \left[\begin{array}{ccc}4&-7\\9&2\end{array}\right] - 3 \left[\begin{array}{ccc}-1&3\\0&-4\end{array}\right] \\ \\ \left[\begin{array}{ccc}16&-28\\36&8\end{array}\right] - \left[\begin{array}{ccc}-3&9\\0&-12\end{array}\right] = \left[\begin{array}{ccc}19&-37\\36&20\end{array}\right]_2$