Типовой расчет № 6 Векторы. Базис. Разложение по базису Задание 1
Даны координаты
точек
в системе координат
.
Найти координаты векторов
,
,
,
.
Проверить, что векторы (
)
образуют базис и найти разложение
вектора
по этому базису.
№ |
|
|
|
|
|
1 |
(1; 1; 1) |
(3; 6; 7) |
(1; 5; 3) |
(0; 4; –1) |
(0; 7; 3) |
2 |
(–1; 0; 2) |
(6; 8; 1) |
(6; 5; 4) |
(4; 4; 5) |
(7; 10; 6) |
3 |
(2; –3; 4) |
(–1; 1; 6) |
(8; –6; 5) |
(4; –5; 4) |
(–7; 1; 4) |
4 |
(–2; 4; 3) |
(3; 7; –1) |
(–3; 3; –3) |
(–5; 0; –1) |
(–4; –3; 5) |
5 |
(–1;–2; 8) |
(1; –5; 9) |
(5; –1; 7) |
(3; 1; 6) |
(1; 2; 5) |
6 |
(0;–4; –6) |
(2; –5; –4) |
(5; –5; –10) |
(5; –1; –12) |
(7; 6; –14) |
7 |
(10; 0; 2) |
(17;10; –12) |
(15; 1; –1) |
(11; –4; 2) |
(10; –4; –6) |
8 |
(7; 2; 0) |
(12; 2; –2) |
(10; 9; –10) |
(8; 8; –7) |
(9; 6; –3) |
9 |
(0;2; –10) |
(–3; –4; –8) |
(1; 0;–10) |
(–1; 7; –15) |
(–8; 15;–23) |
10 |
(1; 0; 8) |
(–2; –4; 11) |
(0; 1; –13) |
(4; 5; –10) |
(9; 9; –7) |
11 |
(11; 4; 0) |
(12;16; –15) |
(10; 7; –4) |
(7; 6; –1) |
(2; 16; –10) |
12 |
(8; 6; –2) |
(8; 12; –5) |
(6; 19; –13) |
(4; 10; –8) |
(0; –2; –1) |
13 |
(–7; 1; 1) |
(–7; 5; 4) |
(–3; 9; 2) |
(–5; 6; –6) |
(–9; 4; –19) |
14 |
(3; 5; 9) |
(3; 11; 13) |
(1; 5; 11) |
(5; 9; 5) |
(13; 23; –3) |
15 |
(–8;3; –1) |
(–10; 5; –2) |
(–8;14; –13) |
(-5; 6; –10) |
(–1; –8; –5) |
16 |
(0; 7; 7) |
(7; 14; 2) |
(5; 21; –6) |
(3; 12; 5) |
(6; 1; 22) |
17 |
(11; 5; 6) |
(15; 3; 11) |
(19; 7; 9) |
(17; 14; 10) |
(17; 26; 17) |
18 |
(3; 1; –2) |
(7; 1; 4) |
(–2; 1; –1) |
(–1; –1; 1) |
(5; –5; 11) |
19 |
(4; –1; 0) |
(10; 1; 11) |
(7; 3; 9) |
(5; –5; 0) |
(7; –19; –7) |
20 |
(14; 3; 8) |
(16; -3; 10) |
(26; 1; 18) |
(23; 3; 16) |
(19; 1; 14) |
21 |
(4; –5; 2) |
(2; –3; 0) |
(5; 7; –3) |
(1; –1; 2) |
(–9;–15; 10) |
22 |
(–2; 1; 3) |
(0; –2; 4) |
(7; 5; –2) |
(4; –3; 2) |
(0; –22; 11) |
23 |
(0; 5; 2) |
(1; –1; 3) |
(4; 6; –5) |
(1; –1; –1) |
(–4; –21; 8) |
24 |
(–2; 2;–1) |
(0; 0; –5) |
(3; –3; 2) |
(4; –1; 2) |
(8; 1; –2) |
25 |
(0; –5; 2) |
(–1; –3; 2) |
(4; 0; –2) |
(1; –2; 2) |
(–6; –4; 10) |
26 |
(3; 2; –1) |
(4; 2; 0) |
(5; –2; 3) |
(–1; 2; 3) |
(–12; 10; 4) |
27 |
(–3; 0; 1) |
(–1; 4; –4) |
(2; –2; 0) |
(3; –3; –1) |
(7; –1; –8) |
28 |
(1; 2; –2) |
(3; 6; –5) |
(0; 4; 5) |
(–3; 3; 1) |
(–7; 5; –10) |
29 |
(1; 0; –3) |
(6; 0; –5) |
(2; –1; –1) |
(5; 5; –8) |
(16; 17;–24) |
30 |
(–3; 2; 5) |
(–5; 5; 6) |
(1; –2; 3) |
(–3; 8; –2) |
(13; 31;–11) |