Приложение
Попытаемся
самостоятельно ещё раз проанализировать
ход мыслей «суперзвезды» Лены Гладковой,
отвечающей на вопрос, является ли система
уравнений
|
8x1 + 6x2 + 5x3 + 2x4 = 21 |
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3x1 + 3x2 + 2x3 + x4 = 10 |
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4x1 + 2x2 + 3x3 + x4 = 8 |
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3x1 + 5x2 + x3 + x4 = 15 |
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7x1 + 4x2 + 5x3 + 2x4 = 18 |
совместной
(Пример 7)
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8 |
6 |
5 |
2 |
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0 |
2 |
-1 |
0 |
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0 |
2 |
-1 |
0 |
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3 |
3 |
2 |
1 |
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0 |
-2 |
1 |
0 |
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0 |
0 |
0 |
0 |
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A= |
4 |
2 |
3 |
1 |
~ |
4 |
2 |
3 |
1 |
~ |
4 |
2 |
3 |
1 |
~ |
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3 |
5 |
1 |
1 |
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3 |
5 |
1 |
1 |
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3 |
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1 |
1 |
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7 |
4 |
5 |
2 |
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7 |
4 |
5 |
2 |
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7 |
4 |
5 |
2 |
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0 |
-2 |
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0 |
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0 |
-2 |
1 |
0 |
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0 |
-2 |
1 |
0 |
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~ |
4 |
2 |
3 |
1 |
~ |
4 |
0 |
4 |
1 |
~ |
0 |
0 |
4 |
1 |
~ |
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3 |
5 |
1 |
1 |
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3 |
5 |
1 |
1 |
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-1 |
5 |
1 |
1 |
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7 |
4 |
5 |
2 |
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7 |
4 |
5 |
2 |
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-1 |
4 |
5 |
2 |
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-1 |
5 |
1 |
1 |
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-1 |
5 |
1 |
-1 |
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0 |
1 |
-4 |
-1 |
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~ |
-1 |
4 |
5 |
2 |
~ |
-1 |
4 |
5 |
0 |
~ |
-1 |
4 |
5 |
0 |
~ |
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0 |
-2 |
1 |
0 |
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0 |
-2 |
1 |
0 |
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0 |
-2 |
1 |
0 |
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0 |
0 |
4 |
1 |
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0 |
0 |
4 |
1 |
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0 |
0 |
4 |
1 |
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0 |
-1 |
4 |
1 |
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0 |
-1 |
0 |
0 |
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0 |
-1 |
0 |
0 |
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~ |
-1 |
0 |
7 |
0 |
~ |
-1 |
0 |
7 |
0 |
~ |
-1 |
0 |
7 |
0 |
~ |
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0 |
-2 |
1 |
0 |
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0 |
-2 |
1 |
0 |
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0 |
0 |
1 |
0 |
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0 |
0 |
4 |
1 |
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0 |
0 |
4 |
1 |
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0 |
0 |
4 |
1 |
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0 |
1 |
0 |
0 |
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0 |
1 |
0 |
0 |
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1 |
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0 |
0 |
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~ |
1 |
0 |
7 |
0 |
~ |
1 |
0 |
0 |
0 |
~ |
0 |
1 |
0 |
0 |
=> rA=4 |
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0 |
0 |
1 |
0 |
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0 |
0 |
1 |
0 |
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0 |
0 |
1 |
0 |
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0 |
0 |
0 |
1 |
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0 |
0 |
0 |
1 |
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0 |
0 |
0 |
1 |
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8 |
6 |
5 |
2 |
21 |
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0 |
2 |
-1 |
0 |
5 |
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0 |
-2 |
1 |
0 |
5 |
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3 |
3 |
2 |
1 |
10 |
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0 |
-2 |
1 |
0 |
-5 |
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0 |
0 |
0 |
0 |
0 |
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B= |
4 |
2 |
3 |
1 |
8 |
~ |
4 |
2 |
3 |
1 |
8 |
~ |
4 |
2 |
3 |
1 |
8 |
~ |
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3 |
5 |
1 |
1 |
15 |
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3 |
5 |
1 |
1 |
15 |
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3 |
5 |
1 |
1 |
15 |
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7 |
4 |
5 |
2 |
18 |
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7 |
4 |
5 |
2 |
18 |
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7 |
4 |
5 |
2 |
18 |
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0 |
-2 |
1 |
0 |
-5 |
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0 |
-2 |
1 |
0 |
1 |
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0 |
0 |
1 |
0 |
1 |
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~ |
4 |
0 |
4 |
1 |
3 |
~ |
4 |
0 |
0 |
1 |
3 |
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1 |
0 |
0 |
1 |
3 |
~ |
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3 |
5 |
1 |
1 |
15 |
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3 |
5 |
-2 |
1 |
0 |
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0 |
1 |
-2 |
1 |
0 |
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7 |
4 |
5 |
2 |
18 |
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7 |
4 |
-2 |
2 |
6 |
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1 |
0 |
-2 |
2 |
6 |
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0 |
0 |
1 |
0 |
1 |
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0 |
0 |
1 |
0 |
1 |
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0 |
0 |
1 |
0 |
1 |
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~ |
1 |
0 |
0 |
0 |
0 |
~ |
1 |
0 |
0 |
0 |
0 |
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1 |
0 |
0 |
0 |
0 |
~ |
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0 |
1 |
0 |
1 |
0 |
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0 |
1 |
0 |
0 |
0 |
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0 |
1 |
0 |
0 |
0 |
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1 |
0 |
-2 |
1 |
3 |
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1 |
0 |
-2 |
1 |
3 |
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1 |
0 |
0 |
1 |
3 |
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0 |
0 |
1 |
0 |
1 |
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1 |
0 |
0 |
0 |
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~ |
1 |
0 |
0 |
0 |
0 |
~ |
0 |
1 |
0 |
0 |
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=> rB=4 |
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0 |
1 |
0 |
0 |
0 |
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0 |
0 |
1 |
0 |
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0 |
0 |
0 |
1 |
0 |
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0 |
0 |
0 |
1 |
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rB = rA = 4, следовательно система совместна.