Question

1 - Determine o produto entre as matrizes abaixo e o Determinante
desse produto

|4 5 7 |
A= |0 -2 1 |
|8 3 9 |

B=
| 3 1 6 |
|-6 0 -1|
| -5 7 4|

preciso do cálculo
dou nota máxima pra resposta​

Answer 1

$\boxed{\begin{array}{l}\sf O~produto~de~matrizes~existe~somente \\\sf quando~o~n\acute umero~de~colunas~da~1^a~matriz\\\sf\acute e~igual~ao~n\acute umero~de~linhas~da~2^a~matriz.\\\sf A~matriz~resultante~tem~o~n\acute umero~de~linhas\\\sf da~1^a~e~o~n\acute umero~de~colunas~da~2^a.\\\sf o~produto~\acute e~feito~multiplicando~as~linhas~da~1^a\\\sf pelas~colunas~da~2^a\end{array}}$

$\small\boxed{\begin{array}{l}\sf A=\begin{vmatrix}\sf4&\sf6&\sf7\\\sf0&\sf-2&\sf1\\\sf8&\sf3&\sf9\end{vmatrix}~~~B=\begin{vmatrix}\sf3&\sf1&\sf6\\\sf-6&\sf0&\sf1\\\sf-5&\sf7&\sf4\end{vmatrix}\\\\\sf A\cdot B=\begin{vmatrix}\sf4\cdot3+6\cdot(-6)+7\cdot(-5)&\sf4\cdot1+6\cdot0+7\cdot7&\sf4\cdot6+6\cdot1+7\cdot4\\\sf0\cdot3-2\cdot(-6)+1\cdot(-5)&\sf0\cdot1-2\cdot0+1\cdot7&\sf0\cdot6-2\cdot1+1\cdot4\\\sf8\cdot3+3\cdot(-6)+9\cdot(-5)&\sf8\cdot1+3\cdot0+9\cdot7&\sf8\cdot6+3\cdot1+9\cdot4\end{vmatrix}\end{array}}$

$\small\boxed{\begin{array}{l}\sf A\cdot B=\begin{vmatrix}\sf-53&\sf53&\sf47\\\sf7&\sf7&\sf6\\\sf-39&\sf71&\sf81\end{vmatrix}\\\sf det(A\cdot B)=-53\cdot(141)-53\cdot(801)+47\cdot(770)\\\sf det(A\cdot B)=-7473-42453+36190\\\sf det(A\cdot B)=-13736\end{array}}$