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Консультация № 175549
22.12.2009, 21:16
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Уважаемые эксперты, не могу решить следующую задачу:
При каком условии некоторая линейная комбинация любых решений данной неоднородной системы линейных уравнений будет решением этой системы?
При каком условии некоторая линейная комбинация любых решений данной неоднородной системы линейных уравнений будет решением этой системы?
Обсуждение
22.12.2009, 22:17
общий
это ответ
Здравствуйте, Adskiy.
Пусть X1, X2, …, Xn – решения неоднородной системы линейных уравнений. Тогда сумма α1X1 + α2X2 + … + αnXn также будет решением этой системы, если α1 + α2 + … + αn = 1 (α1, α2, ..., αn - числа).
Такой пример приводится в Сборнике задач по высшей математике (Т. 1) авторов К. Н. Лунгу, Д. Т. Письменного, С. Н. федина, Ю. А. Шевченко...
С уважением.
Пусть X1, X2, …, Xn – решения неоднородной системы линейных уравнений. Тогда сумма α1X1 + α2X2 + … + αnXn также будет решением этой системы, если α1 + α2 + … + αn = 1 (α1, α2, ..., αn - числа).
Такой пример приводится в Сборнике задач по высшей математике (Т. 1) авторов К. Н. Лунгу, Д. Т. Письменного, С. Н. федина, Ю. А. Шевченко...
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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