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Консультация № 194407
12.01.2019, 18:40
0.00 руб.
0
3
1
Здравствуйте! Прошу помощи в следующем вопросе:
Исследуйте на линейную зависимость систему векторов. В случае линейной зависимости, найдите какую-либо зависимость.
ā1=(1;2;-1;0), ā2=(-1;1;0;2), ā3=(-2;1;1;0), ā4=(-1;1;1;1).
Исследуйте на линейную зависимость систему векторов. В случае линейной зависимости, найдите какую-либо зависимость.
ā1=(1;2;-1;0), ā2=(-1;1;0;2), ā3=(-2;1;1;0), ā4=(-1;1;1;1).
Обсуждение
16.01.2019, 06:28
общий
это ответ
Здравствуйте, Лилия!
Заданная система векторов линейно независима, если существуют такие вещественные числа
не все равные нулю, что
При этом определённой должна быть система уравнений
коэффициентами которой являются координаты векторов заданной системы, записанные в соответствующих столбцах.
Поскольку ранг основной матрицы
системы уравнений
равен четырём ( её определитель 
в чём можно убедиться выполнив либо "ручной" расчёт, либо воспользовавшись MS Excel), то есть совпадает с числом неизвестных, постольку у этой системы нет ненулевых решений (см., например, теорему 1 здесь). Соответственно, заданная система векторов линейно независима.
Расчёт определителя находится здесь.
Заданная система векторов линейно независима, если существуют такие вещественные числа
не все равные нулю, чтоПри этом определённой должна быть система уравнений
коэффициентами которой являются координаты векторов заданной системы, записанные в соответствующих столбцах.
Поскольку ранг основной матрицы
системы уравнений
равен четырём ( её определитель в чём можно убедиться выполнив либо "ручной" расчёт, либо воспользовавшись MS Excel), то есть совпадает с числом неизвестных, постольку у этой системы нет ненулевых решений (см., например, теорему 1 здесь). Соответственно, заданная система векторов линейно независима.Расчёт определителя находится здесь.
5
Большое спасибо за помощь.
Об авторе:
Facta loquuntur.
Facta loquuntur.
16.01.2019, 07:27
общий
Большое спасибо. Я как раз в решении дошла до матрицы.
нужно ли в данном вопросе доказывать что векторы не коллинеарны.
нужно ли в данном вопросе доказывать что векторы не коллинеарны.
16.01.2019, 08:15
общий
Адресаты:
Лилия нужно ли в данном вопросе доказывать что векторы не коллинеарны.
Не нужно.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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