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Консультация № 199850
11.12.2020, 23:05
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
"Проверить совместимость системы уравнений и в случае совместности решить её по правилу Крамера: (система уравнений сверху->вниз) 2x1-x2-3x3=0 3x1+4x2+2x3=1 x1+5x2+x3=-3" Спасибо.
"Проверить совместимость системы уравнений и в случае совместности решить её по правилу Крамера: (система уравнений сверху->вниз) 2x1-x2-3x3=0 3x1+4x2+2x3=1 x1+5x2+x3=-3" Спасибо.
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Обсуждение
16.12.2020, 16:13
общий
это ответ
Здравствуйте, Alex!
Запишем систему в матричной форме:
где
Условие совместности системы имеет вид
В данном случае для матрицы A минором наибольшего, третьего порядка является её определитель
отличный от нуля. Он так же является минором наибольшего порядка для расширенной матрицы A|B. Следовательно,
и система совместна. Её решение получаем методом Крамера, вычислив соответствующие определители:
Запишем систему в матричной форме:
где
Условие совместности системы имеет вид
В данном случае для матрицы A минором наибольшего, третьего порядка является её определитель
отличный от нуля. Он так же является минором наибольшего порядка для расширенной матрицы A|B. Следовательно,
и система совместна. Её решение получаем методом Крамера, вычислив соответствующие определители:
5
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