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EXÁMEN MATEMÁTICAS I Matrices y geometria
1º Clasifica el siguiente sistema según los valores que puede tomar "a". Resuelve el sistema para el caso a = 6.
2º Resolver la siguiente ecuación matricial: X·B + B = B-1, siendo:
B =
3º Se sabe que
= 100. Explicando qué propiedades de los determinantes seutilizan y sin desarrollar el determinante, hallar el valor de:
4º Estudiar según los valores del parámetro a, la posición relativa de las rectas r y s de ecuaciones:
r
s
5º Determinar los valores de los parámetros a y b para las rectas se corten ortogonalmente:
r:
s:
6ºHallar el punto de la recta x= -2y = -2z, cuya distancia al origen es el doble que su distancia a la recta:
RESPUESTAS EXÁMEN
1º
A =
A* =
2·F2 -F4
= F1-2F3; F2+3F3
= 11F1+3F2
= -2
= 2·(1·11)·(-12+2·a) =0
12 = 2·a => a = 6
Si a = 6
= 0 Rg A* = 3 Rg A = 3 S.C.D.
Si a
6
0 Rg A* = 4 Rg A = 3 S.I.
Si a = 6
=
= -3 - 6 = -9
x =
=
=
= 5
y =
=
= 4
z =
=
=
= 2
SOLUCIÓN (5, 4, 2)
2º
X·B + B = B-1 B =
X·B = B-1 - B
X = (B-1- B)·B-1 = (B-1)2 - B·B-1 = (B-1)2 - I
=
(1 -1 +1 + 1 + 1 + 1) =
= 2
Adj B =
=
=
Adj Bt =
B-1=
(B-1)2 =
(B-1)2 - I =
-
=
3º
= 100
= 2
= 2·
= -2
= -2·100 = -200
= -
=
= -
=
= 100
4º
r
A = (0, 1, a)
s
B = (a, 2, a)
= (a, 1, 0)
Rg (
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Enviado por: | Maite |
Idioma: | castellano |
País: | España |