Advanced Math Archive: Questions from June 07, 2024
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1.- (20 puntos) Considera la matriz
A=[[1,-1,1,-1],[0,1,-1,0],[1,-1,1,1],[-1,0,0,-1]]
. a) (10 puntos) Calcular
det(A^(3))
. b) (10 puntos) Calcular
det(A^(-1))
. 2.- (20 puntos) Considera la matriz
B
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Definir
A=([1,0,0],[0,\omega ,0],[0,0,\omega
^(2)]),
dónde
\omega =i
y definir
x=P(C)
como el espacio de polinomios sobre
C
. Considere el operador
T(p)=p(A)
, para
pinx
; este operador asigna polino
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