Задача 2
У просторі R3 задано п’ять векторів:
,
,
,
,
.
Потрібно:
знайти три вектори, що утворюють базис, і розкласти інші вектори в цьому базисі;
перейти до нового базису і знайти координати розкладу інших векторів у новому базисі.
№ |
|
|
|
|
|
№ |
|
|
|
|
|
1 |
2 |
3 |
–1 |
1 |
0 |
2 |
9 |
2 |
1 |
0 |
–4 |
–1 |
–1 |
–1 |
–1 |
–1 |
–3 |
–1 |
–1 |
–1 |
3 |
||
2 |
2 |
3 |
2 |
3 |
5 |
2 |
2 |
3 |
–8 |
||
3 |
0 |
3 |
2 |
1 |
3 |
4 |
0 |
3 |
2 |
–1 |
1 |
–1 |
–3 |
–1 |
–1 |
1 |
–1 |
0 |
–1 |
1 |
–1 |
||
3 |
8 |
2 |
2 |
–5 |
3 |
–2 |
2 |
–3 |
2 |
||
5 |
–1 |
1 |
0 |
–1 |
2 |
6 |
–1 |
–3 |
1 |
1 |
–1 |
1 |
–1 |
–1 |
3 |
–1 |
3 |
8 |
–4 |
–2 |
1 |
||
–3 |
2 |
3 |
–7 |
2 |
0 |
–2 |
–1 |
2 |
–3 |
||
7 |
–5 |
–1 |
1 |
–1 |
7 |
8 |
–1 |
–5 |
–1 |
1 |
3 |
16 |
3 |
–2 |
1 |
15 |
1 |
10 |
3 |
–2 |
–2 |
||
1 |
0 |
2 |
–3 |
10 |
–3 |
–8 |
0 |
2 |
11 |
||
№ |
|
|
|
|
|
№ |
|
|
|
|
|
9 |
–1 |
2 |
–1 |
3 |
1 |
10 |
3 |
1 |
–1 |
–3 |
–1 |
1 |
–1 |
3 |
–6 |
–2 |
–6 |
–2 |
1 |
8 |
3 |
||
–3 |
8 |
0 |
5 |
2 |
5 |
2 |
–3 |
–3 |
0 |
||
11 |
3 |
5 |
–9 |
1 |
–7 |
12 |
21 |
3 |
1 |
–7 |
7 |
–2 |
–3 |
6 |
–1 |
5 |
14 |
–2 |
–1 |
5 |
–6 |
||
–5 |
–9 |
16 |
–1 |
12 |
36 |
–5 |
–1 |
12 |
11 |
||
13 |
–7 |
–9 |
3 |
1 |
25 |
14 |
–7 |
18 |
3 |
5 |
1 |
5 |
7 |
–2 |
–1 |
18 |
5 |
13 |
–2 |
–4 |
–1 |
||
12 |
15 |
–5 |
–1 |
42 |
12 |
30 |
–5 |
–8 |
–1 |
||
15 |
5 |
1 |
–7 |
7 |
3 |
16 |
–1 |
–3 |
5 |
1 |
3 |
–4 |
–1 |
5 |
–4 |
–2 |
2 |
5 |
–7 |
–1 |
–4 |
||
–8 |
–1 |
12 |
14 |
–5 |
0 |
–2 |
7 |
2 |
5 |
||
17 |
–9 |
–1 |
1 |
3 |
–1 |
18 |
3 |
3 |
–1 |
1 |
–9 |
15 |
2 |
–1 |
–4 |
0 |
–4 |
–3 |
2 |
–1 |
13 |
||
–7 |
0 |
2 |
5 |
–6 |
5 |
8 |
0 |
2 |
13 |
||
19 |
3 |
–6 |
–1 |
–1 |
1 |
20 |
–1 |
1 |
3 |
–7 |
–1 |
–4 |
9 |
2 |
1 |
–1 |
1 |
–1 |
–4 |
9 |
2 |
||
5 |
–8 |
0 |
–3 |
2 |
–3 |
2 |
5 |
11 |
0 |
||
21 |
0 |
–1 |
0 |
1 |
–1 |
22 |
0 |
0 |
1 |
–1 |
4 |
1 |
3 |
–2 |
–1 |
0 |
6 |
1 |
–1 |
0 |
–5 |
||
–1 |
0 |
3 |
–2 |
4 |
–7 |
–1 |
–2 |
4 |
–9 |
||
23 |
–1 |
–3 |
0 |
1 |
4 |
24 |
–1 |
3 |
0 |
2 |
1 |
0 |
3 |
1 |
–1 |
0 |
0 |
0 |
1 |
–2 |
–1 |
||
4 |
8 |
–1 |
–2 |
15 |
4 |
11 |
–1 |
–5 |
–2 |
||
25 |
2 |
1 |
–1 |
–2 |
0 |
26 |
–1 |
–3 |
3 |
1 |
1 |
–2 |
–1 |
0 |
4 |
1 |
0 |
–1 |
3 |
1 |
2 |
||
–5 |
–2 |
4 |
1 |
–1 |
–3 |
–8 |
7 |
2 |
2 |
||
27 |
–7 |
–1 |
1 |
1 |
3 |
28 |
1 |
–1 |
–1 |
1 |
–3 |
–3 |
0 |
1 |
2 |
–2 |
2 |
3 |
0 |
1 |
–5 |
||
19 |
–3 |
2 |
2 |
9 |
2 |
–4 |
–3 |
2 |
–7 |
||
29 |
1 |
–2 |
–1 |
1 |
1 |
30 |
1 |
1 |
1 |
–5 |
–1 |
2 |
–3 |
0 |
–1 |
1 |
–1 |
1 |
2 |
–5 |
0 |
||
2 |
–5 |
–3 |
3 |
2 |
3 |
2 |
2 |
11 |
–3 |
