Question

16. Considere as matrizes [ A=left[egin{array}{ll} frac{1}{2} & 0 \ 0 & frac{1}{2} end{array} ight], A^{2}=A cdot A, A^{3}=A^{2} . A, ldots ldots, A^{n}=A^{n-1} . A, ldots ldots . ] Se ( d_{n} ) é o determinante da matriz ( A^{n} ), então, a soma ( d_{1}+d_{2}+d_{3}+ldots ldots . .+d_{n}+ldots . . ). é igual a A) ( frac{1}{3} ). B) ( frac{1}{2} ). C) ( frac{2}{3} ). D) ( frac{3}{4} ).

          16. Considere as matrizes
[
A=left[egin{array}{ll}
frac{1}{2} & 0 \
0 & frac{1}{2}
end{array}
ight], A^{2}=A cdot A, A^{3}=A^{2} . A, ldots ldots, A^{n}=A^{n-1} . A, ldots ldots .
]

Se ( d_{n} ) é o determinante da matriz ( A^{n} ), então, a soma ( d_{1}+d_{2}+d_{3}+ldots ldots . .+d_{n}+ldots . . ). é igual a
A) ( frac{1}{3} ).
B) ( frac{1}{2} ).
C) ( frac{2}{3} ).
D) ( frac{3}{4} ).

$16. Considere as matrizes [ A=left[eginarrayll frac12 0 0 frac12 endarray ight], A^2=A cdot A, A^3=A^2 . A, ldots ldots, A^n=A^n-1 . A, ldots ldots . ] Se ( dn ) é o determinante da matriz ( A^n ), então, a soma ( d1+d2+d3+ldots ldots . .+dn+ldots . . ). é igual a A) ( frac13 ). B) ( frac12 ). C) ( frac23 ). D) ( frac34 ).$

Added by Amigos P.

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