Question

× -× × -x

Sendo A= 2 +2 e B= 2 -2

______ ________

2 2 O VALOR DO DETERMINANTE DA MATRIZ [A B]

[B A] i

Igual a= ?

Answer 1

$Det(M)~=~a~.~a~-~b~.~b\\\\\\Det(M)~=~\frac{2^x~+~2^{-x}}{2}\,.\,\frac{2^x~+~2^{-x}}{2}~-~\frac{2^x~-~2^{-x}}{2}\,.\,\frac{2^x~-~2^{-x}}{2}\\\\\\Det(M)~=~\frac{2^x\,.\,2^x~+~2^x\,.\,2^{-x}~+~2^x\,.\,2^{-x}~+~2^{-x}2^{-x}}{4}~-~\frac{2^x\,.\,2^x~-~2^{x}\,.\,2^{-x}~-~2^{x}\,.\,2^{-x}~+~2^{-x}\,.\,2^{-x}}{4}\\\\\\Det(M)~=~\frac{\left(2^{x+x}~+~2~.~2^{x+(-x)}~+~2^{-x+(-x)}\right)}{4}~-~\frac{\left(2^{x+x}~-~2~.~2^{x+(-x)}~+~2^{-x+(-x)}\right)}{4}$

$Det(M)~=~\frac{\left(2^{2x}~+~2~.~2^{0}~+~2^{-2x}\right)~-~\left(2^{2x}~-~2~.~2^{0}~+~2^{-2x}\right)}{4}\\\\\\Det(M)~=~\frac{2^{2x}~+~2~.~1~+~2^{-2x}~-~2^{2x}~+~2~.~1~-~2^{-2x}}{4}\\\\\\Det(M)~=~\frac{2+2}{4}\\\\\\\boxed{Det(M)~=~1}$