- •Решить матричным способом систему уравнений
- •Методом Гаусса исследовать и решить данные системы. В случае бесконечного множества решений найти общее решение и одно какое-либо частное решение.
- •3. Коллинеарны ли вектора и ?
- •4. Исследовать на линейную зависимость систему векторов
- •6. Найти собственные значения и собственные векторы матрицы:
- •7. Найти все линейные зависимости между пятью трехмерными векторами
4. Исследовать на линейную зависимость систему векторов
п/п |
|||||||||||
1 |
1 |
4 |
6 |
1 |
-1 |
1 |
1 |
1 |
3 |
||
2 |
2 |
-3 |
1 |
3 |
-1 |
5 |
1 |
-4 |
3 |
||
3 |
5 |
4 |
3 |
3 |
3 |
2 |
8 |
1 |
3 |
||
4 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
||
5 |
1 |
-1 |
2 |
-1 |
1 |
-1 |
2 |
-1 |
1 |
||
6 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
||
7 |
1 |
1 |
1 |
1 |
2 |
3 |
1 |
3 |
6 |
||
8 |
3 |
4 |
-5 |
8 |
7 |
-2 |
2 |
-1 |
8 |
||
9 |
3 |
2 |
-4 |
4 |
1 |
-2 |
5 |
2 |
-3 |
||
10 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
||
11 |
5 |
-6 |
1 |
3 |
-5 |
-2 |
2 |
-1 |
3 |
||
12 |
7 |
1 |
-3 |
2 |
2 |
-4 |
3 |
-3 |
5 |
||
13 |
1 |
2 |
3 |
6 |
5 |
9 |
7 |
8 |
9 |
||
14 |
2 |
1 |
0 |
-5 |
0 |
3 |
3 |
4 |
3 |
||
15 |
-2 |
1 |
5 |
4 |
-3 |
0 |
0 |
-1 |
10 |
||
16 |
2 |
0 |
2 |
1 |
-1 |
0 |
0 |
-1 |
-2 |
||
17 |
2 |
3 |
1 |
-1 |
0 |
-1 |
2 |
2 |
2 |
||
18 |
3 |
2 |
1 |
2 |
3 |
4 |
3 |
1 |
-1 |
||
19 |
1 |
5 |
2 |
-1 |
1 |
-1 |
1 |
1 |
1 |
||
20 |
1 |
-1 |
-3 |
3 |
2 |
1 |
2 |
3 |
4 |
||
21 |
3 |
3 |
1 |
1 |
-2 |
1 |
1 |
1 |
1 |
||
22 |
3 |
1 |
-1 |
2 |
-1 |
0 |
5 |
2 |
-1 |
||
23 |
4 |
3 |
1 |
1 |
-2 |
1 |
2 |
2 |
2 |
||
24 |
4 |
3 |
1 |
6 |
7 |
4 |
2 |
0 |
-1 |
||
25 |
3 |
2 |
1 |
1 |
-3 |
-7 |
1 |
2 |
3 |
||
26 |
3 |
7 |
2 |
-2 |
0 |
-1 |
2 |
2 |
1 |
||
27 |
1 |
-2 |
6 |
1 |
0 |
1 |
2 |
-6 |
17 |
||
28 |
6 |
3 |
4 |
-1 |
-2 |
-1 |
2 |
1 |
2 |
||
29 |
7 |
3 |
4 |
-1 |
-2 |
-1 |
4 |
2 |
4 |
||
30 |
2 |
3 |
2 |
4 |
7 |
5 |
2 |
0 |
-1 |
5. Написать разложение вектора по векторам .
п/п |
||||||||||||
1 |
-2 |
4 |
7 |
0 |
1 |
2 |
1 |
0 |
1 |
-1 |
2 |
4 |
2 |
6 |
12 |
-1 |
1 |
3 |
0 |
2 |
-1 |
1 |
0 |
-1 |
2 |
3 |
1 |
-4 |
4 |
2 |
1 |
-1 |
0 |
3 |
2 |
1 |
-1 |
1 |
4 |
-9 |
5 |
5 |
4 |
1 |
1 |
2 |
0 |
-3 |
-1 |
2 |
1 |
5 |
-5 |
-5 |
5 |
-2 |
0 |
1 |
1 |
3 |
-1 |
0 |
4 |
1 |
6 |
13 |
2 |
7 |
5 |
1 |
0 |
2 |
-1 |
3 |
1 |
0 |
-1 |
7 |
-19 |
-1 |
7 |
0 |
1 |
1 |
-2 |
0 |
1 |
3 |
1 |
0 |
8 |
3 |
-3 |
4 |
1 |
0 |
2 |
0 |
1 |
1 |
2 |
-1 |
4 |
9 |
3 |
3 |
-1 |
3 |
1 |
0 |
-1 |
2 |
1 |
-1 |
0 |
2 |
10 |
-1 |
7 |
-4 |
-1 |
2 |
1 |
2 |
0 |
3 |
1 |
1 |
-1 |
11 |
6 |
5 |
-14 |
1 |
1 |
4 |
0 |
-3 |
2 |
2 |
1 |
-1 |
12 |
6 |
-1 |
7 |
1 |
-2 |
0 |
-1 |
1 |
3 |
1 |
0 |
4 |
13 |
5 |
15 |
0 |
1 |
0 |
5 |
-1 |
3 |
2 |
0 |
-1 |
1 |
14 |
2 |
-1 |
11 |
1 |
1 |
0 |
0 |
1 |
-2 |
1 |
0 |
3 |
15 |
11 |
5 |
-3 |
1 |
0 |
2 |
-1 |
0 |
1 |
2 |
5 |
-3 |
16 |
8 |
0 |
5 |
2 |
0 |
1 |
1 |
1 |
0 |
4 |
1 |
2 |
17 |
3 |
1 |
8 |
0 |
1 |
3 |
1 |
2 |
-1 |
2 |
0 |
-1 |
18 |
8 |
1 |
12 |
1 |
2 |
-1 |
3 |
0 |
2 |
-1 |
1 |
1 |
19 |
-9 |
-8 |
-3 |
1 |
4 |
1 |
-3 |
2 |
0 |
1 |
-1 |
2 |
20 |
-5 |
9 |
-13 |
0 |
1 |
-2 |
3 |
-1 |
1 |
4 |
1 |
0 |
21 |
-15 |
5 |
6 |
0 |
5 |
1 |
3 |
2 |
-1 |
-1 |
1 |
0 |
22 |
8 |
9 |
4 |
1 |
0 |
1 |
0 |
-2 |
1 |
1 |
3 |
0 |
23 |
23 |
-14 |
-30 |
2 |
1 |
0 |
1 |
-1 |
0 |
-3 |
2 |
5 |
24 |
3 |
1 |
3 |
2 |
1 |
0 |
1 |
0 |
1 |
4 |
2 |
1 |
25 |
-1 |
7 |
0 |
0 |
3 |
1 |
1 |
-1 |
2 |
2 |
-1 |
0 |
26 |
11 |
-1 |
4 |
1 |
-1 |
2 |
3 |
2 |
0 |
-1 |
1 |
1 |
27 |
0 |
-8 |
9 |
0 |
-2 |
1 |
3 |
1 |
-1 |
4 |
0 |
1 |
28 |
8 |
-7 |
-13 |
0 |
1 |
5 |
3 |
-2 |
1 |
-1 |
0 |
1 |
29 |
2 |
7 |
5 |
1 |
0 |
1 |
1 |
-2 |
0 |
0 |
3 |
1 |
30 |
15 |
-20 |
-1 |
0 |
2 |
1 |
0 |
1 |
-1 |
5 |
-3 |
2 |