Задание 4
Решить системы методом Жордана – Гаусса
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Задание 5
Найти общее решение для каждой из данных систем и проанализировать его структуру (указать базис пространства решений однородной системы, установить размерность пространства, выделить частное решение неоднородной системы).
1 3x1+x2-4x3+2x4+x5=0 2x1-2x2-3x3-7x4+2x5=0 x1+11x2+34x4-5x5=0 |
x1+2x2-2x3-3x4=4 2x1+5x2-x3-4x4=9 x1+3x2+x3-x4=5 |
2 7x1+2x2-x3-2x4+2x5=0 x1-3x2+x3-x4-x5=0 2x1+3x2+2x3+x4+x5=0 |
x1-4x2+2x3+3x4=5 2x1-7x2+4x3+x4=9 x1-3x2+2x3+x4-3x5=4 |
3 x1+x2+10x3+x4-x5=0 5x1-x2+8x3-2x4+2x5=0 3x1-3x2-12x3-4x4+4x5=0 |
x1+2x2-3x3-4x4=1 3x1+7x2-2x3-x4=4 2x1+5x2+x3+3x4=3 |
4 6x1-9x2+21x3-3x4-12x5=0 -4x1+6x2-14x3+2x4+8x5=0 2x1-3x2+7x3-x4-4x5=0 |
x1-5x2+3x3+4x4=4 2x1-9x2+2x3+x5=7 x1-4x2-x3-4x4+x5=3 |
5 2x1-2x2+2x3-x4+x5=0 x1+10x2-3x3-2x4-x5=0 4x1+19x2-4x3-5x4-x5=0 |
x1+3x2-x3-2x4=1 2x1+7x2-4x3-3x4=3 x1+4x2-3x3-x4=2 |
6 5x1-2x2+9x3-4x4-x5=0 x1+4x2+2x3+2x4-5x5=0 6x1+2x2+11x3-2x4-6x5=0 |
x1+x2+4x3+2x5=0 3x1+4x2+x3+3x4=1 2x1+3x2-3x3+3x4-2x5=1 |
7 12x1-x2+7x3+11x4-x5=0 24x1-2x2+14x3+22x4-2x5=0 x1+x2+x3-x4+2x5=0 |
x1-2x2+2x3+3x4=0 2x1-3x2+x3+4x4=1 3x1-5x2+3x3+7x4=1 |
8 x1+2x2+x3+4x4+x5=0 2x1+x2+3x3+x4-5x5=0 x1+3x2-x3+6x4-x5=0 |
x1-x2+4x3+3x4=0 3x1-2x2+x3+3x5=1 2x1-x2-3x3-3x4+2x5=1 |
9 2x1+3x2+3x3-3x4-x5=0 x1+6x2-x3+x4+2x5=0 x1+16x2-6x3+6x4+7x5=0 |
x1-2x2+2x3+3x4=0 3x1-5x2+x3+4x4=1 2x1-3x2-x3+x4=1 |
10 x1+2x2-x3+x4-x5=0 x1+x2+2x3-x4+x5=0 2x1+3x2+x3=0 |
x1-3x2+4x3+3x5=2 3x1-8x2+x3+2x4=5 2x1-5x2-3x3+2x4-3x5=3 |
11 8x1+x2+x3-x4+2x5=0 3x1-3x2-2x3+x4-3x5=0 5x1+4x2+3x3-2x4+5x5=0 |
x1-3x2+x3+2x4=4 2x1-5x2+4x3+3x4=7 x1-2x2+3x3+x4=3 |
12 x1+3x2-x3+12x4-x5=0 2x1-2x2+x3-10x4+x5=0 3x1+2x2+2x4=0 |
x1-x2+3x3+4x4=0 4x1-3x2+x3+2x5=1 3x1-2x2-2x3-4x4+2x5=1
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13 7x1-14x2+3x3-x4+x5=0 x1-2x2+x3-3x4+7x5=0 5x1-10x2+x3+5x4-13x5=0 |
x1+4x2-2x3-3x4=2 2x1+9x2-x3-4x4=5 x1+5x2+x3-x4=3 |
14 x1+2x2+3x3+x4-x5=0 2x1-2x2-6x3-4x4+x5=0 3x1-2x2+3x3+3x4-x5=0 |
x1-2x2+3x3+4x5=1 4x1-7x2+2x3+4x4=3 3x1-5x2-x3+x4-4x5=2 |
15 x1+x2+x3-x4-x5=0 2x1+x2-2x3-x4-2x5=0 x1+2x2+5x3-2x4-x5=0 |
x1-x2+3x3+4x4=0 2x1-x2+2x3+x4=1 4x1-3x2+8x3+9x4=1 |
16 2x1+2x2-2x3+x4-3x5=0 3x1-x2+2x3-x4+2x5=0 x1-3x2+4x3-2x4+5x5=0 |
x1+x2-3x3-4x4=1 4x1+5x2-2x3-x5=3 3x1+4x2+x3+4x4-x5=2 |
17 x1+2x2-3x3+10x4-x5=0 -x1-2x2+3x3+10x4+x5=0 x1+6x2-9x3+30x4-3x5=0 |
x1-4x2+2x3+3x4=5 2x1-7x2+4x3+x4=9 x1-3x2+2x3-2x4=4 |
18 2x1+x2-x3+7x4+5x5=0 x1-2x2+3x3-5x4-7x5=0 3x1-x2+2x3+2x4-2x5=0 |
x1+2x2-2x3-3x5=4 2x1+5x2-x3-4x4=9 x1+3x2+x3-4x4+3x5=5 |
19 2x1-2x2-3x3-7x4+2x5=0 x1+11x2+34x4-5x5=0 x1-5x2-2x3-16x4+3x5=0 |
x1-5x2+3x3+4x4=4 2x1-9x2+2x3+x4=7 x1-4x2-x3-3x4=3 |
20 3x1+x2-8x3+2x4+x5=0 x1+11x2-12x3-5x5=0 x1-5x2+2x3+x4+3x5=0 |
x1+2x2-3x3-4x4=1 3x1+7x2-2x3+x5=4 2x1+5x2+x3+4x4+x5=3 |
21 x1+3x2-5x3+9x4-x5=0 2x1+7x2-3x3-7x4+2x5=0 x1+4x2+2x3-16x4+3x5=0 |
x1+x2+4x3+2x4=0 3x1+4x2+x3+3x4=1 2x1+3x2-3x3+x4=1 |
22 5x1+2x2-x3+3x4+4x5=0 3x1+x2-3x3+3x4+4x5=0 6x1+3x2-2x3+4x4+5x5=0 |
x1+3x2-x3-2x5=1 2x1+7x2-4x3-3x4=3 x1+4x2-3x3-3x4+2x5=2 |
23 3x1+2x2-2x3-x4+4x5=0 7x1+5x2-3x3-2x4+x5=0 x1+x2+x3-7x5=0 |
x1-x2+4x3+3x4=0 3x1-2x2+x3+2x4=1 2x1-x2-3x3-x4=1 |
24 6x1+3x2-2x3+4x4+7x5=0 7x1+4x2-3x3+2x4+4x5=0 x1+x2-x3-2x4-3x5=0 |
x1-2x2+2x3+3x4=0 2x1-3x2+x3+4x5=1 3x1-5x2+3x3+3x4+4x5=1 |
25 3x1-5x2+2x3+5x4=0 7x1-4x2+x3+3x4=0 5x1+7x2-4x3-9x4=0 |
x1-3x2+4x3+3x4=2 3x1-8x2+x3+2x4=5 2x1-5x2-3x3-x4=3 |
26 x1+x2+3x3-2x4+3x5=0 2x1+2x2+5x3-x4+3x5=0 x1+x2+4x3-5x4+6x5=0 |
x1-2x2+2x3+3x5=0 3x1-5x2+x3+4x4=1 2x1-3x2-x3+4x4-3x5=1 |
27 x1+2x2+3x3-2x4+x5=0 x1+2x2+7x3-4x4+x5=0 x1+2x2+11x3-6x4+x5=0 |
x1-x2+3x3+4x4=1 4x1-3x2+x3+2x4=1 3x1-2x2-2x3-2x4=1 |
28 6x1+3x2+2x3+3x4+4x5=0 4x1+2x2+x3+2x4+3x5=0 2x1+x2+x3+x4+x5=0 |
x1-3x2+x3+2x4=4 2x1-5x2+4x3+3x5=7 x1-2x2+3x3-2x4+3x5=3 |
29 3x1+2x2+4x3+x4+2x5=0 3x1+2x2-2x3+x4=0 3x1+2x2+16x3+x4+6x5=0 |
x1-2x2+3x3+4x4=1 4x1-7x2+2x3+x4=3 3x1-5x2-x3-3x4=2 |
30 x1+x2+x3+2x4+x5=0 x1-2x2-3x3+x4-x5=0 2x1-x2-2x3+3x4=0 |
x1+4x2-2x3-3x5=2 2x1+9x2-x3-4x4=5 x1+5x2+x3-4x4+3x5=3 |