Advanced Math Archive: Questions from June 12, 2024
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Para las matrices
A=([2,3],[-1,2]),B=([4,1],[0,6]),C=([-5,1,2],[2,0,6])
, verificar que todas las operaciones están bien definidas, y se
cumplen las igualdades: i.
(A+B)*C=A*C+B*C
ii.
(A*B)*C=A*(B*C)
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Usar el método de eliminación de Gauss para hallar la inversa
de: a.
([1,2,3],[1,1,2],[2,4,7])
b.
([-1,1,1],[2,0,-1],[2,-1,-1])
c.
([1,6,2],[-2,3,5],[7,12,-4])
d.
([1,0,2,0],[-1,1,0,0],[1,0,0,1],[0,
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Ya se probó que el conjunto
B={([1],[0],[3]),([2],[2],[1]),([3],[4],[1])}
es base de
R^(3)
. Explicar por qué el conjunto
C={([1],[0],[3]),([2],[2],[1]),([3],[4],[1]),([0],[0],[0])}
no es base, a pe
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Decidir si el vector
vec(w)=([2],[1],[2])
es autovector de la matriz
A=([3,2,4],[2,0,2],[4,2,3])
, y si lo es, asociado a qué autovalor.
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Reactivo 2: Considere el sistema dado por
[[x_(1)^(˙)],[x_(2)^(˙)],[x_(3)^(˙)]]=[[2,0,0],[0,2,0],[0,3,1]][[x_(1)],[x_(2)],[x_(2)]]+[[0,1],[1,0],[0,1]][[u_(1)],[u_(2)]];[[y_(1)],[y_(2)]]=[[1,0,0],[0
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masa y centro de masa
R=el
triangulo de vertices, usando integrales, cambio en el orden de
integracion y una grafica
(0,0),(3,0),(3,5)\rho (x,y)=x R: m=15kg,
c((9)/(4),(15)/(8))
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