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Консультация № 139349
06.06.2008, 18:08
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Уважаемые эксперты у меня возник вопрос. Вопрос из части высшей математики. Тема : Нахождение определителя n-го порядка. Еще на парах сам решал а теперь просто на просто забыл. Ладно, в общем, у меня дан определитель -
| 3 2 0 -5 |
| 4 3 -5 0 |
| 1 0 -2 3 |
| 0 1 -3 4 |
мне нужно вычислить определитель разложив его по элементам итого столбца и житой строки. i = 2 j= 4, я все бы смог сделать, но есть одно, чего я не понимаю. Допустим мы начинаем решать по итой строке
(?)*(-1)^3
*
2 0 -5
0 -2 3
1 -3 4
+(?) * (-1)^4...
Так вот там где я поставил знак вопроса там какоето число, но откуда оно берется я так и не понял...
Пожалуйста обьясните мне. Искренне надеюсь на вашу помощь. Заранее спасибо.
| 3 2 0 -5 |
| 4 3 -5 0 |
| 1 0 -2 3 |
| 0 1 -3 4 |
мне нужно вычислить определитель разложив его по элементам итого столбца и житой строки. i = 2 j= 4, я все бы смог сделать, но есть одно, чего я не понимаю. Допустим мы начинаем решать по итой строке
(?)*(-1)^3
*
2 0 -5
0 -2 3
1 -3 4
+(?) * (-1)^4...
Так вот там где я поставил знак вопроса там какоето число, но откуда оно берется я так и не понял...
Пожалуйста обьясните мне. Искренне надеюсь на вашу помощь. Заранее спасибо.
Обсуждение
07.06.2008, 03:16
общий
это ответ
Здравствуйте, Пашков Дмитрий Владимирович!
Если в указанном Вами определителе delta четвертого порядка вычеркнуть вторую строку (i = 2) и четвертый столбец (j = 4), на пересечении которых находится элемент a(24) (в скобки заключены нижние индексы), и сдвинуть оставшиеся ряды, то получится определитель третьего порядка, который называется минором исходного определителя, соответствующим элементу a(24), и обозначается delta(24). Формула разложения, которую Вы, по-моему, имеете в виду выглядит так:
delta = S (от i=1 до i=n) a(ij)*[(-1)^(i+j)]*delta(ij),
то есть интересующее Вас число - элемент a(ij).
С уважением.
Если в указанном Вами определителе delta четвертого порядка вычеркнуть вторую строку (i = 2) и четвертый столбец (j = 4), на пересечении которых находится элемент a(24) (в скобки заключены нижние индексы), и сдвинуть оставшиеся ряды, то получится определитель третьего порядка, который называется минором исходного определителя, соответствующим элементу a(24), и обозначается delta(24). Формула разложения, которую Вы, по-моему, имеете в виду выглядит так:
delta = S (от i=1 до i=n) a(ij)*[(-1)^(i+j)]*delta(ij),
то есть интересующее Вас число - элемент a(ij).
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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