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Консультация № 202498
31.03.2022, 14:17
0.00 руб.
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Haйти мaтpицy пepexoдa oт бaзиca a1, a2, a3 к бaзиcy в1, в2, в3. Пo yкaзaнным paзлoжeниям этиx вeктopoв в бaзиce e1, e2, e3.
а1= 3 е1 + 2 е2 + е3
а2= е1 - 2 е2 + е3
а3= 2 е1 + 2 е2 + 3 е3
в1= е1 + е2
в2= е1 - е3
в3= е1 + е2 + е3
Haйти мaтpицy пepexoдa oт бaзиca a1, a2, a3 к бaзиcy в1, в2, в3. Пo yкaзaнным paзлoжeниям этиx вeктopoв в бaзиce e1, e2, e3.
а1= 3 е1 + 2 е2 + е3
а2= е1 - 2 е2 + е3
а3= 2 е1 + 2 е2 + 3 е3
в1= е1 + е2
в2= е1 - е3
в3= е1 + е2 + е3
Обсуждение
01.04.2022, 22:09
общий
это ответ
Здравствуйте, Виктор!
Для решения предложенной Вам задачи я воспользовался примером здесь: Ссылка >>.
Определим матрицу перехода от базиса
к базису 
Запишем координаты векторов в виде строк матрицы и приведём полученную матрицу к ступенчатому виду. Справа от матрицы указываются векторы и регистрируются проводимые преобразования матрицы (получилось не очень удачно из-за особенностей редактора формул портала).
Нулевым строкам ступенчатого вида матрицы соответствуют равенства
Из этих равенств получим, что
Записав коэффициенты полученного разложения в виде столбцов, получим искомую матрицу перехода
Для решения предложенной Вам задачи я воспользовался примером здесь: Ссылка >>.
Определим матрицу перехода от базиса
к базису Запишем координаты векторов в виде строк матрицы и приведём полученную матрицу к ступенчатому виду. Справа от матрицы указываются векторы и регистрируются проводимые преобразования матрицы (получилось не очень удачно из-за особенностей редактора формул портала).
Нулевым строкам ступенчатого вида матрицы соответствуют равенства
Из этих равенств получим, что
Записав коэффициенты полученного разложения в виде столбцов, получим искомую матрицу перехода
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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