Задание №8
Доказать, что векторы а, b, c образуют базис (линейно независимы), и найти разложение вектора х по этому базису.
-
1.
x = (2, 4, 7),
a = (0, 1, 2),
b = (1, 0, 1),
c = (1, 2, 4).
2.
x = (6, 12,1),
a = (1, 3, 0),
b = (2, 1, 1),
c = (0, 1, 2).
3.
x = (1, 4, 4),
a = (2, 1, 1),
b = (0, 3, 2),
c = (1, 1, 1).
4.
x = (9, 5, 5),
a = (4, 1, 1),
b = (2, 0, 3),
c = (1, 2, 1).
5.
x = (5,5, 5),
a = (2, 0, 1),
b = (1, 3, 1),
c = (0, 4, 1).
6.
x =(19,1, 7),
a = (0, 1, 1),
b = (2, 0, 1),
c = (3, 1, 0).
7.
x = (3, 3, 4),
a = (1, 0, 2),
b = (0, 1, 1),
c = (2, 1, 4).
8.
x = (1, 7,4),
a = (1, 2, 1),
b = (2, 0, 3),
c = (1, 1, 1).
9.
x = (3, 3, 1),
a = (3, 1, 0),
b = (1, 2, 1),
c = (1, 0, 2).
10.
x = (5, 15, 0),
a = (1, 0, 5),
b = (1, 3, 2),
c = (0, 1, 1).
11.
x = (3, 1, 8),
a = (0, 1, 3),
b = (2, 1, -1),
c = (2, 0, -1).
12.
x = (-1, 2,4),
a = (2, 3, 1),
b = (0, 0, 2),
c = (-3, 0, 4).
13.
x = (7, 1, 9),
a = (5, 1, 2),
b = (8, 1, -3),
c = (-1, 3, 2).
14.
x = (3, 5, 7),
a = (1, 3, -3),
b = (-4, 1, 5),
c = (2, 1, 6).
15.
x = (2,1, 5),
a = (1, 4, 2),
b = (1, -3, 1),
c = (-1, 1, 0).
16.
x =(6,22, 23),
a = (1, 5, 10),
b = (1, 4, 5),
c = (1, 3, 1).
17.
x = (1, 2, -3),
a = (1, 8, -4),
b = (1, 3, -1),
c = (-1, 6, 3).
18.
x = (9, 4,18),
a = (4, 2, 5),
b = (-3, 5, 6),
c = (2, 3, 2).
19.
x = (-1, -4, 2),
a = (1, 2, 4),
b = (1, -1, 1),
c = (2, 2, 4).
20.
x = (4, -23, 0),
a = (2, 5, 3),
b = (1, 2, -1),
c = (5, 13, 5).
21.
x = (8, -1, 0),
a = (3, 2, 1),
b = (4, -1, 5),
c = (2, -3, 1).
22.
x = (4, 1, 8),
a = (1, 3, 2),
b = (2, 5, 7),
c = (1, 3, -1).
23.
x = (6, 20, 6),
a = (1, 2, 3),
b = (-2, 3, -2),
c = (3, 4, -5).
24.
x = (4, 11, 11),
a = (2, 3, 3),
b = (-1, 4, 2),
c = (1, -2, 4).
25.
x = (5,11, 11),
a = (3, 2, 2),
b = (2, 3, 1),
c = (1, 1, 3).
26.
x =(3, 5, 7),
a = (1, 3, -3),
b = (4, 1, 5),
c = (-2, 1, 6).
27.
x = (1, 2, 3),
a = (1, 8, 4),
b = (1, 3, 1),
c = (-1, 6, -3).
28.
x = (9, 4, 18),
a = (4, 2, 5),
b = (-3, 5, 6),
c = (2, -3, 2).
29.
x = (6, 3, 5),
a = (1, 2, 1),
b = (1, -1, -1),
c = (1, 1, 2).
30.
x = (15, 15, 36),
a = (7, 5, 10),
b = (2, -3, -11),
c = (3, 2, 5).