Question

sejam A= { -4 3 } { 1 2} e B= {1 0 } { -1 3} caucule o determinante da seguinte matriz A + 2B

Answer 1

$A = \left[\begin{array}{ccc}-4&3\\1&2\end{array}\right]_2 \\ \\ \\ B = \left[\begin{array}{ccc}1&0\\-1&3\end{array}\right]_2 \\ \\ \\ det\: ( A + 2B) = \left|\begin{array}{ccc}-4&3\\1&2\end{array}\right| + 2 \left|\begin{array}{ccc}1&0\\-1&3\end{array}\right| \\ \\ \\ det\:(A + 2B) = \left|\begin{array}{ccc}-4&3\\1&2\end{array}\right| + \left|\begin{array}{ccc}2&0\\-2&6\end{array}\right| \\ \\ \\ det\: (A + 2B) = \left|\begin{array}{ccc}-2&3\\-1&8\end{array}\right| = -16 - (-3) = -13$