Question

Dadas as matrizes calcule o determinante do produto ​

Answer 1

Resposta:

Alternativa e) 6

Explicação:

Produto das matrizes:

$\left[\begin{array}{ccc}2&3\\1&3\end{array}\right] .\left[\begin{array}{ccc}2&4\\1&3\end{array}\right]=\left[\begin{array}{ccc}(2*2)+(3*1)&(2*4)+(3*3)\\(1*2)+(3*1)&(1*4)+(3*3)\end{array}\right] \\\\\\\left[\begin{array}{ccc}2&3\\1&3\end{array}\right] .\left[\begin{array}{ccc}2&4\\1&3\end{array}\right] = \left[\begin{array}{ccc}7&17\\5&13\end{array}\right]$

Logo,

$A*B = \left[\begin{array}{ccc}7&17\\5&13\end{array}\right]$

Calculando o determinante:

Det = Diagonal principal - Diagonal secundária

$Det = 7*13 - 17*5\\Det = 91 - 85\\Det = 6$