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Консультация № 191207
30.06.2017, 04:40
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Прикрепленные файлы:
Обсуждение
30.06.2017, 11:04
общий
это ответ
Здравствуйте, asdf1234!
5.1. По-моему, линейная зависимость заданных векторов следует из теоремы о линейной зависимости любых четырёх векторов трёхмерного евклидова пространства (см. здесь п. 4).
5.2. Вычислим смешанное произведение заданных векторов:
значит, заданные векторы образуют базис.
Матрица
перехода от старого базиса к новому имеет вид
Вычислим обратную матрицу
перехода от нового базиса к старому. Имеем
Вычислим координаты (компоненты) вектора
в новом базисе:
То есть в новом базисе
5.1. По-моему, линейная зависимость заданных векторов следует из теоремы о линейной зависимости любых четырёх векторов трёхмерного евклидова пространства (см. здесь п. 4).
5.2. Вычислим смешанное произведение заданных векторов:
значит, заданные векторы образуют базис.
Матрица
перехода от старого базиса к новому имеет видВычислим обратную матрицу
перехода от нового базиса к старому. ИмеемВычислим координаты (компоненты) вектора
в новом базисе:То есть в новом базисе
Об авторе:
Facta loquuntur.
Facta loquuntur.
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