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Консультация № 184893
21.12.2011, 09:04
62.26 руб.
0
1
1
Здравствуйте, уважаемые эксперты! Помогите,пожалуйста,с линейной алгеброй:
Требуется найти собственные значения и собственные векторы матрицы
6 6 6
3 3 3
1 1 1
Помощь нужна до завтра!
У уважением,
Иван.
Требуется найти собственные значения и собственные векторы матрицы
6 6 6
3 3 3
1 1 1
Помощь нужна до завтра!
У уважением,
Иван.
Обсуждение
21.12.2011, 14:43
общий
это ответ
Здравствуйте, Барс Иван!
Приравниваем определитель характеристической матрицы к 0:
|6-k 6 6|
|3 3-k 3|=0
|1 1 1-k|
(6-k)(3-k)(1-k)+18+18-6(3-k)-3(6-k)-18(1-k)=0
10k^2-k^3=0
k1=k2=0, k3=10
Собственные значения матрицы 0 и 10. Найдем соответствующие им собственные векторы:
k=0:
СЛАР для нахождения координат собственного вектора
6х+6y+6z=0
3х+3y+3z=0
х+y+z=0
Решение: (x;y;-x-y), где х и у - любые числа
k=10:
СЛАР для нахождения координат собственного вектора
-4х+6y+6z=0
3х-7y+3z=0
х+y-9z=0
Решение: (x;x/2;x/6), где х - любое число
Приравниваем определитель характеристической матрицы к 0:
|6-k 6 6|
|3 3-k 3|=0
|1 1 1-k|
(6-k)(3-k)(1-k)+18+18-6(3-k)-3(6-k)-18(1-k)=0
10k^2-k^3=0
k1=k2=0, k3=10
Собственные значения матрицы 0 и 10. Найдем соответствующие им собственные векторы:
k=0:
СЛАР для нахождения координат собственного вектора
6х+6y+6z=0
3х+3y+3z=0
х+y+z=0
Решение: (x;y;-x-y), где х и у - любые числа
k=10:
СЛАР для нахождения координат собственного вектора
-4х+6y+6z=0
3х-7y+3z=0
х+y-9z=0
Решение: (x;x/2;x/6), где х - любое число
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