7. Разложение векторов по векторам базиса
Даны две системы
векторов
Определить,
какая из этих систем образует базис;
разложить вектор
по этому базису. Координаты векторов
приведены в таблице.
№ |
|
|
|
|
|
|
|
1 |
(3, 4, 1) |
(2, -1, 0) |
(-2, 3, 1) |
(2, 3, 1) |
(-1, 1, 2) |
(3, 7, 4) |
(4, 7, 1) |
2 |
(5, -1, 4) |
(1, 2, 3) |
(4, -2, 1) |
(1, -1, 2) |
(2, 1, 1) |
(4, -1, 5) |
(1, 4, 3) |
3 |
(2, 0, -1) |
(3, -5, 4) |
(0, 0, 2) |
(1, 1, 1) |
(-2, 3, 0) |
(-3, 7, 1) |
(3, -5, 6) |
4 |
(-1, 1, 3) |
(1, 3, 1) |
(2, -1, -1) |
(-3, 1, -1) |
(1, -1, 1) |
(-1, -1, 1) |
(-3, 5, 8) |
5 |
(-5, 7, 4) |
(1, 3, 1) |
(2, -1, -1) |
(5, 2, 3) |
(1, 0, 5) |
(2, 1, -1) |
(0, 8, 3) |
6 |
(1, 0, 1) |
(-1, 1, 2) |
(3, 5, 1) |
(2, -1, 3) |
(1, 1, -4) |
(4, 1, -5) |
(2, 1, -2) |
7 |
(2, 1, 3) |
(-1, 0, 1) |
(0, 1, -1) |
(2, -2, 1) |
(-1, 0, 1) |
(-1, -2, 4) |
(5, 3, 10) |
8 |
(1, -2, 1) |
(3, 4, -1) |
(2, 6, 2) |
(2, 2, 3) |
(1, 2, 3) |
(1, 1, 1) |
(3, 0, -2) |
9 |
(4, -2, 3) |
(1, -3, 1) |
(-3, -1, -2) |
(1, 1, 1) |
(0, 1, 1) |
(0, 0, 1) |
(5, 6, -3) |
10 |
(4, 2, 3) |
(1, -3, 1) |
(-2, 0, 2) |
(4, -1, 3) |
(1, 1, -2) |
(7, 2, -3) |
(3, 2, -1) |
11 |
(3, 2, -2) |
(3, -2, -1) |
(1, 1, -1) |
(1, -1, 5) |
(2, 3, -4) |
(1, 2, 1) |
(3, -5, -1) |
12 |
(2, 2, 1) |
(1, -3, 1) |
(-1, 0, 1) |
(-2, 1, -3) |
(2, 4, 8) |
(-2, 6, 2) |
(-3, -5, 1) |
13 |
(3, 0, 5) |
(1, -2, 1) |
(6, -6, 8) |
(1, 0, 0) |
(1, 1, 0) |
(1, 2, 1) |
(3, -5, 1) |
14 |
(2, 3, 1) |
(-1, -3, 4) |
(0, -3, 9) |
(1, 2, 0) |
(0, -3, 0) |
(2, 1, 1) |
(5, -6, 3) |
15 |
(3, -3, 3) |
(1, -3, 2) |
(5, -9, 7) |
(4, 1, -2) |
(2, -3, 0) |
(3, 1, -2) |
(7, -1, -3) |
16 |
(2, 1, -1) |
(2, -3, 0) |
(1, 1, -1) |
(3, -2, -1) |
(1, 1, 5) |
(1, -4, 9) |
(6, -5, 3) |
17 |
(3, 3, 1) |
(2, -2, 1) |
(2, 1, 1) |
(-2, 3, 4) |
(-1, -1, -2) |
(0, 5, 8) |
(1, 0, 5) |
18 |
(1, -1, 7) |
(2, 3, -1) |
(3, 7, -9) |
(2, 1, 4) |
(1, -3, 8) |
(5, 0, 3) |
(0, -3, 1) |
19 |
(0, 3, 0) |
(1, -4, 2) |
(2, 3, 2) |
(1, -2, 3) |
(4, -4, 3) |
(6, -8, 9) |
(-3, 5, 1) |
20 |
(-1, 4, 2) |
(0, -5, 0) |
(2, 3, 2) |
(1, -1, 8) |
(2, -1, 5) |
(3, -2, -2) |
(-2, 3, 4) |
21 |
(3, 2, -2) |
(1, 0, 1) |
(4, -1, 3) |
(1, -3, 4) |
(1, -2, -3) |
(-1, 4, -11) |
(13, 3, 2) |
22 |
(4, 1, 5) |
(1, 3, 4) |
(-2, 2, 1) |
(-2, 1, -2) |
(1, -3, 5) |
(0, -5, 8) |
(5, -5, -1) |
23 |
(5, 1, 2) |
(0, -3, 1) |
(3, 8, 4) |
(2, 3, -8) |
(1, 2, 3) |
(4, 7, -2) |
(2, -10, -1) |
24 |
(3, 3, -8) |
(1, 2, -5) |
(1, -1, 2) |
(2, 1, 0) |
(2, -4, 3) |
(-1, 2, 0) |
(6, 0, 5) |
25 |
(3, 5, 8) |
(-2, 2, 1) |
(-1, 1, 10) |
(2, 0, -1) |
(3, -5, 4) |
(2, 0, 2) |
(3, 1, 0) |
26 |
(3, -1, 0) |
(3, -2, 1) |
(5, -2, 1) |
(4, 1, -3) |
(-1, 3, -1) |
(2, 7, 1) |
(11, -5, 2) |
27 |
(9, 3, -4) |
(2, -1, 3) |
(7, 4, 1) |
(1, -2, 7) |
(3, 1, -4) |
(5, -3, 10) |
(28, 16, 12) |
28 |
(5, -5, 8) |
(1, -5, 7) |
(4, 0, 1) |
(2, 7, 8) |
(1, -3, -5) |
(4, 1, -2) |
(-6, -10, 12) |
29 |
(5, 6, 5) |
(3, -5, 2) |
(2, -1, 3) |
(3, 1, -6) |
(1, -3, 2) |
(5, -5, -2) |
(6, -3, 9) |
30 |
(7, 3, -1) |
(-1, 3, 2) |
(6, 0, 3) |
(1, 1, 4) |
(-2, 3, 1) |
(0, 5, 9) |
(-4,-12,-10) |
