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Консультация № 177412
22.03.2010, 21:01
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здравствуйте эксперты!!!! Ответте пожалуйста на вопрос! Исследуйте систему на совместимость и найдите общее решение системы методом Гауса сделайте проверку!! Заранее благодарен.
x1+x2-x3-2x4=1
2x1-3x2-2x3-4x4=5
x1+2x2-x3-4x4=5
x1+x2-x3-2x4=1
2x1-3x2-2x3-4x4=5
x1+2x2-x3-4x4=5
Обсуждение
22.03.2010, 22:20
общий
24.03.2010, 15:38
это ответ
Здравствуйте, Лялюшкин Александр Николаевич.
Вычитаем из второго уравнения удвоенное первое и из третьего уравнения первое:
x1+x2-x3-2x4=1
-5x2=3
x2-2x4=4
Из второго уравнения находим x2=-3/5, после этого из третьего уравнения находим x4=-23/10.
Осталось первое уравнение, в нем можно задать значение x3 произвольно: x3=C. Тогда из него находим x1=C-3.
Ответ:
Система совместна и общее решение дается формулами:
x1=C-3
x2=-3/5
x3=C
x4=-23/10
где C - произвольная постоянная.
Вычитаем из второго уравнения удвоенное первое и из третьего уравнения первое:
x1+x2-x3-2x4=1
-5x2=3
x2-2x4=4
Из второго уравнения находим x2=-3/5, после этого из третьего уравнения находим x4=-23/10.
Осталось первое уравнение, в нем можно задать значение x3 произвольно: x3=C. Тогда из него находим x1=C-3.
Ответ:
Система совместна и общее решение дается формулами:
x1=C-3
x2=-3/5
x3=C
x4=-23/10
где C - произвольная постоянная.
24.03.2010, 10:21
общий
P.S. Перепишем полученную систему в виде
x1-2x4+x2-x3=1
-2x4+x2=4
-5x2=3
Это есть классическая финальная стадия прямого прохода метода Гаусса. Думаю, что пересталять строки и столбцы все же необязательно.
Отсюда получаем:
x1=C-3
x2=-3/5
x3=C
x4=-23/10
x1-2x4+x2-x3=1
-2x4+x2=4
-5x2=3
Это есть классическая финальная стадия прямого прохода метода Гаусса. Думаю, что пересталять строки и столбцы все же необязательно.
Отсюда получаем:
x1=C-3
x2=-3/5
x3=C
x4=-23/10
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