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Консультация № 190110
21.11.2016, 19:11
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Здравствуйте! У меня возникли сложности с решением данной задачи: 
Заранее большое спасибо!!!
Заранее большое спасибо!!!
Обсуждение
21.11.2016, 22:51
общий
это ответ
Здравствуйте, ms.nastasya2512!
Составим матрицу системы и приведём её к ступенчатому виду:
Ранг последней матрицы равен числу её ненулевых строк, то есть равен двум. Поскольку линейные преобразования строк не изменяют ранга матрицы, постольку и ранг матрицы заданной системы равен двум. Он меньше числа неизвестных, равного четырём, поэтому заданная система линейных уравнений имеет ненулевые решения. К этому же выводу можно прийти, если учесть, что определитель матрицы системы
Последней матрице соответствует система
или
или
Положив
получим общее решение заданной системы уравнений в виде 
Составим матрицу системы и приведём её к ступенчатому виду:
Ранг последней матрицы равен числу её ненулевых строк, то есть равен двум. Поскольку линейные преобразования строк не изменяют ранга матрицы, постольку и ранг матрицы заданной системы равен двум. Он меньше числа неизвестных, равного четырём, поэтому заданная система линейных уравнений имеет ненулевые решения. К этому же выводу можно прийти, если учесть, что определитель матрицы системы
Последней матрице соответствует система
или
или
Положив
получим общее решение заданной системы уравнений в виде
Об авторе:
Facta loquuntur.
Facta loquuntur.
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