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Консультация № 191571
28.10.2017, 20:15
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Здравствуйте! Помогите решить задачу
Доказать что векторы А,В,С(буквы со стрелками) образуют базис и найти координаты вектора D (со стрелкой) в этом базисе А(со стрелкой) [5,3,2], В(со стрелкой) [2,-5,1], С(со стрелкой) [-7,4,-4], D(со стрелкой)
[36,1,15]
Доказать что векторы А,В,С(буквы со стрелками) образуют базис и найти координаты вектора D (со стрелкой) в этом базисе А(со стрелкой) [5,3,2], В(со стрелкой) [2,-5,1], С(со стрелкой) [-7,4,-4], D(со стрелкой)
[36,1,15]
Обсуждение
28.10.2017, 22:03
общий
это ответ
Здравствуйте, Tata1207!
Вычислим смешанное произведение векторов
значит, векторы некомпланарны и образуют базис.
Чтобы вычислить координаты вектора
в этом базисе, нужно решить векторное уравнение
или эквивалентную систему скалярных уравнений
Воспользовавшись формулами Крамера, получим
Следовательно,
Вычислим смешанное произведение векторов
значит, векторы некомпланарны и образуют базис.
Чтобы вычислить координаты вектора
в этом базисе, нужно решить векторное уравнениеили эквивалентную систему скалярных уравнений
Воспользовавшись формулами Крамера, получим
Следовательно,
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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