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Консультация № 199448
28.10.2020, 13:18
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Задание № 2 Решить систему из №1 методом Гаусса
Желательно подробное решение)
Задание № 2 Решить систему из №1 методом Гаусса
Желательно подробное решение)
Обсуждение
01.11.2020, 11:16
общий
это ответ
Здравствуйте, alekseyslobodyanyuk20003!
Запишем расширенную матрицу систему (включающую столбец свободных членов):
Разделим первую строку на элемент первого столбца (1) и вычтем из всех последующих, домножив на соответствующие элементы первого столбца (2 и 3), что позволит обнулить их:
Повторим для второй строки (разделив её на 7 и вычтя из третьей строки, домножив на 4):
Третью строку просто разделим на соответствующий элемент (-58/7):
Получаем верхнюю треугольную матрицу (в которой все элементы ниже главной диагонали равны нулю). Теперь проделываем аналогичные операции "в обратном порядке" (снизу вверх): вычитаем третью строку из остальных, домножив соответственно на -10/7 и 3 (чтобы обнулить остальные элементы третьего столбца):
затем вычитаем вторую строку из первой, домножив на -2:
Получаем единичную матрицу и столбец свободных членов, элементы которого являются решением системы:
Запишем расширенную матрицу систему (включающую столбец свободных членов):
Разделим первую строку на элемент первого столбца (1) и вычтем из всех последующих, домножив на соответствующие элементы первого столбца (2 и 3), что позволит обнулить их:
Повторим для второй строки (разделив её на 7 и вычтя из третьей строки, домножив на 4):
Третью строку просто разделим на соответствующий элемент (-58/7):
Получаем верхнюю треугольную матрицу (в которой все элементы ниже главной диагонали равны нулю). Теперь проделываем аналогичные операции "в обратном порядке" (снизу вверх): вычитаем третью строку из остальных, домножив соответственно на -10/7 и 3 (чтобы обнулить остальные элементы третьего столбца):
затем вычитаем вторую строку из первой, домножив на -2:
Получаем единичную матрицу и столбец свободных членов, элементы которого являются решением системы:
5
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