Решить систему линейных уравнений с помощью обратной матрицы. Для этого предварительно сформировать в соответствии с заданием (таблица 8) матрицу коэффициентов и вектор-столбец свободных членов.
Решить систему уравнений с помощью функции lsolve.
Таблица 8
Системы линейных уравнений
N |
Система уравнений |
N |
Система уравнений |
1 |
4.4 x1-2.5 x2+19.2 x3-10.8 x4=4.3 5.5 x1-9.3 x2-14.2 x3+13.2 x4=6.8 7.1 x1-11.5 x2-5.3 x3+6.7 x4=-1.8 14.2 x1+23.4 x2-8.8 x3+5.3 x4=7.2 |
16 |
30.1 x1-1.4 x2+10 x3-1.5 x4 = 10 17.5 x1+11.1 x2+1.3 x3-7.5 x4 = 1.3 1.7 x1-21.1 x2+7.1 x3-17.1 x4 = 10 2.1 x1-2.1 x2+3.5 x3+3.3 x4 = 1.7 |
2 |
8.2 x1-3.2 x2+14.2 x3+14.8 x4=- 8.4 5.6 x1-12 x2+15 x3-6.4 x4=4.5 5.7 x1+3.6 x2-12.4 x3-2.3 x4=3.3 6.8 x1+13.2 x2-6.3 x3-8.7 x4=14.3 |
17 |
7.3 x1-8.1 x2+12.7 x3-6.7 x4 = 8.8 11.5 x1+6.2 x2-8.3 x3+9.2 x4 = 21.5 8.2 x1-5.4 x2+4.3 x3-2.5 x4 = 6.2 2.4 x1+11.5 x2-3.3 x3+14.2 x4= -6.2 |
3 |
5.7 x1-7.8 x2-5.6 x3-8.3 x4=2.7 6.6 x1+13.1 x2-6.3 x3+4.3 x4= - 5.5 14.7 x1-2.8 x2+5.6 x3-12.1 x4= 8.6 8.5 x1+12.7 x2-23.7 x3+5.7 x4= 14.7 |
18 |
4.8 x1+12.5 x2-6.3 x3-9.7 x4 = 3.5 22 x1-31.7 x2+12.4 x3-8.7 x4 = 4.6 15.2 x1-21.1 x2-4.5 x3+14.4 x4 = 15 8.6 x1-14.4 x2+6.2 x3+2.8 x4 = - 1.2 |
4 |
3.8 x1+14.2 x2+6.3 x3-15.5 x4 = 2.8 8.3 x1-6.6 x2+5.8 x3+12.2 x4= - 4.7 6.4 x1-8.5 x2-4.3 x3+8.8 x4= 7.7 17.1 x1-8.3 x2+14.4 x3- 7.2 x4= 13.5 |
19 |
6.4 x1+7.2 x2-8.3 x3+42 x4 = 2.23 5.8 x1-8.3 x2+14.3 x3-6.2 x4 = 17.1 8.6 x1+7.7 x2-18.3 x3+8.8 x4 = - 5.4 13.2 x1-5.2 x2-6.5 x3+12.2 x4 = 6.5 |
5 |
15.7 x1+6.6 x2-5.7 x3+11.5 x4= - 2.4 8.8 x1-6.7 x2+5.5 x3-4.5 x4= 5.6 6.3 x1-5.7 x2-23.4 x3+6.6 x4= 7.7 14.3 x1+8.7 x2-15.7 x3-5.8 x4= 23.4 |
20 |
14.2 x1+3.2 x2-4.2 x3+8.5 x4 = 13.2 6.3 x1-4.3 x2+12.7 x3-5.8 x4 = - 4.4 8.4 x1-22.3 x2-5.2 x3+4.7 x4 = 6.4 2.7 x1+13.7 x2+6.4 x3-12.7 x4 = 8.5 |
Окончание таблицы 8 |
|||
N |
Система уравнений |
N |
Система уравнений |
6 |
4.3 x1-12.1 x2+23.2 x3-14.13x4=15.5 2.4 x1-4.4 x2+3.5 x3+5.5 x4 = 2.5 5.4 x1+8.3 x2-7.4 x3-12.7 x4 = 8.6 6.3 x1-7.6 x2+1.34 x3+3.7 x4 = 12.1 |
21 |
7.3 x1-12.4 x2-3.8 x3-14.3 x4 = 5.8 10.7 x1-7.7 x2+12.5 x3+6.6 x4= -6.6 15.6 x1+6.6 x2+14.4 x3-8.7 x4=12.4 7.5 x1+12.2 x2-8.3 x3+3.7 x4 = 9.2 |
7 |
14.4 x1-5.3 x2+14.3 x3-12.7 x4=-14.4 23.4 x1-14.2 x2-5.4 x3+2.1 x4 = 6.6 6.3 x1-13.2 x2-6.5 x3+14.3 x4 = 9.4 5.6 x1+8.8 x2-6.7 x3-23.8 x4 = 7.3 |
22 |
13.2 x1-8.3 x2-4.4 x3+6.2 x4 = 6.8 8.3 x1+4.2 x2-5.6 x3+7.7 x4 = 12.4 5.8 x1-3.7 x2+12.4 x3-6.2 x4 = 8.7 3.5 x1+6.6 x2-13.8 x3-9.3 x4= - 10.8 |
8 |
1.7 x1+10 x2-1.3 x3+2.1 x4 = 3.1 3.1 x1+1.7 x2-2.1 x3+5.4 x4 = 2.1 3.3 x1-7.7 x2+4.4 x3-5.1 x4 = 1.9 10 x1-20.1 x2+20.4 x3+1.7 x4 = 1.8 |
23 |
8.1 x1+1.2 x2-9.1 x3+1.7 x4 = 10 1.1 x1-1.7 x2+7.2 x3-3.4 x4 = 1.7 1.7 x1-1.8 x2+10 x3+2.3 x4 = 2.1 1.3 x1+1.7 x2-9.9 x3+3.5 x4 = 27.1 |
9 |
1.7 x1-1.8 x2+1.9 x3-57.4 x4 = 10 1.1 x1-4.3 x2+1.5 x3-1.7 x4 = 19 1.2 x1+1.4 x2+1.6 x3+1.8 x4 = 20 7.1 x1-1.3 x2-4.1 x3+5.2 x4 = 10 |
24 |
3.3 x1-2.2 x2-10 x3+1.7 x4 = 1.1 1.8 x1+21.1 x2+1.3 x3-2.2 x4 = 2.2 10 x1+1.1 x2+20 x3-4.5 x4 = 10 70 x1-1.7 x2-2.2 x3+3.3 x4 = 2.1 |
10 |
6.1 x1+6.2 x2-6.3 x3+6.4 x4 = 6.5 1.1 x1-1.5 x2+2.2 x3-3.8 x4 = 4.2 5.1 x1-5.0 x2+4.9 x3-4.8 x4 = 4.7 1.8 x1+1.9 x2+2.0 x3-2.1 x4 = 2.2 |
25 |
1.7 x1+9.9 x2-20 x3-1.7 x4 = 1.7 20 x1+0.5 x2-30.1 x3-1.1 x4 = 2.1 10 x1-20 x2+30.2 x3+0.5 x4 = 1.8 3.3 x1-0.7 x2+3.3 x3+20 x4 = - 1.7 |
11 |
2.2 x1-3.1 x2+4.2 x3-5.1 x4 = 6.01 1.3 x1+2.2 x2-1.4 x3+1.5 x4 = 10 6.2 x1-7.4 x2+8.5 x3-9.6 x4=1.1 1.2 x1+1.3 x2+1.4 x3+4.5 x4 = 1.6 |
26 |
1.7 x1-1.3 x2-1.1 x3-1.2 x4 = 2.2 10 x1-10 x2-1.3 x3+1.3 x4 = 1.1 3.5 x1+3.3 x2+1.2 x3+1.3 x4 = 1.2 1.3 x1+1.1 x2-1.3 x3-1.1 x4 = 10 |
12 |
35.8 x1+2.1 x2-34.5 x3-11.8 x4 = 0.5 27.1 x1-7.5 x2+11.7 x3-23.5 x4 =12.8 11.7 x1+1.8 x2-6.5 x3+7.1 x4 = 1.7 6.3 x1+10 x2+7.1 x3+3.4 x4 = 20.8 |
27 |
1.1 x1+11.3 x2-1.7 x3+1.8 x4 = 10 1.3 x1-11.7 x2+1.8 x3+1.4 x4 = 1.3 1.1 x1-10.5 x2-1.7 x3-1.5 x4 = 1.1 1.5 x1-0.5 x2+1.8 x3-1.1 x4 = 10 |
13 |
35.1 x1+1.7 x2+37.5 x3-2.8 x4 = 7.5 45.2 x1+21.1 x2-1.1 x3-1.2 x4 = 11.1 -21.1 x1+31.7 x2+1.2 x3-1.5 x4 = 2.1 31.7 x1+18.1 x2-31.7 x3+2.2 x4 = 0.5 |
28 |
1.4 x1+2.1 x2-3.3 x3+1.1 x4 = 10 10 x1-1.7 x2+1.1 x3-1.5 x4 = 1.7 2.2 x1+34.4 x2-1.1 x3-1.2 x4 = 20 1.1 x1+1.3 x2+1.2 x3+1.4 x4 = 1.3 |
14 |
1.1 x1+11.2 x2+11.1 x3-13.1 x4 = 1.3 -3.3 x1+1.1 x2+30.1 x3-20.1 x4 = 1.1 7.5 x1+1.3 x2+1.1 x3+10 x4 = 20 1.7 x1+7.5 x2-1.8 x3+2.1 x4 = 1.1 |
29 |
1.3 x1-1.7 x2+3.3 x3+1.7 x4 = 1.1 10 x1+5.5 x2-1.3 x3+3.4 x4 = 1.3 1.1 x1+1.8 x2-2.2 x3-1.1 x4 = 10 1.3 x1-1.2 x2+2.1 x3+2.2 x4 = 1.8 |
15 |
7.5 x1+1.8 x2-2.1 x3+7.7 x4 = 1.1 10 x1+1.3 x2-20 x3-1.4 x4 = 1.5 2.8 x1-1.7 x2+3.9 x3+4.8 x4 = 1.2 10 x1+31.4 x2-2.1 x3-10 x4 = - 1.1 |
30 |
1.2 x1+1.8 x2-2.2 x3-4.1 x4 = 1.3 10 x1-5.1 x2+1.2 x3+5.5 x4 = 1.2 2.2 x1-30.1 x2+3.1 x3+5.8 x4 = 10 10 x1+2.4 x2-30.5 x3-2.2 x4 = 34.1 |
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