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Консультация № 191570
28.10.2017, 20:09
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Здравствуйте! Помогите решить задачу
Проверить совместность системы уравнений и в случае совместности решить ее по правилу Крамера
3x1+X2-X3=-4
-3x1 +5x2 +6x3 =36
X1-4x2-2x3 =-19
Проверить совместность системы уравнений и в случае совместности решить ее по правилу Крамера
3x1+X2-X3=-4
-3x1 +5x2 +6x3 =36
X1-4x2-2x3 =-19
Обсуждение
28.10.2017, 21:32
общий
это ответ
Здравствуйте, Tata1207!
Запишем расширенную матрицу системы
Запишем матрицу системы
и вычислим её определитель
Ранг определителя матрицы системы равен трём, значит, ранг матрицы системы равен трём. Этот определитель является минором расширенной матрицы системы, значит, ранг расширенной матрицы системы тоже равен трём.
Ранг расширенной матрицы системы равен рангу матрицы системы. Согласно теореме Кронекера - Капелли, система совместна.
Вычислим по формулам Крамера
Запишем расширенную матрицу системы
Запишем матрицу системы
и вычислим её определитель
Ранг определителя матрицы системы равен трём, значит, ранг матрицы системы равен трём. Этот определитель является минором расширенной матрицы системы, значит, ранг расширенной матрицы системы тоже равен трём.
Ранг расширенной матрицы системы равен рангу матрицы системы. Согласно теореме Кронекера - Капелли, система совместна.
Вычислим по формулам Крамера
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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