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Консультация № 155046
20.12.2008, 02:38
0.00 руб.
0
1
1
!(2-a) (19) ( 30)!
!(0) (-5-a) (-12)!
!(0) (2 ) ( 5-a)! матрица
Найти собственное значение и собственный вектор матрицы при a=2
Приложение:
как сумел нарисовал матрицу 3х3
!(0) (-5-a) (-12)!
!(0) (2 ) ( 5-a)! матрица
Найти собственное значение и собственный вектор матрицы при a=2
Приложение:
как сумел нарисовал матрицу 3х3
Обсуждение
Неизвестный
20.12.2008, 14:07
общий
это ответ
Здравствуйте, миша мухин!
! -L 19 30 !
det ! 0 -7-L -12 ! = -L*((-7-L)*(3-L) + 2*12) = -L*(L^2+4*L+3) = -L*(L+3)*(L+1)
! 0 2 3-L!
Значит, собственные значения равны L1 = 0, L2 = -1, L3 = -3.
Найдём собственный вектор при L = 0 :
Система уравнений : 19*x2 + 30*x3 = 0; -7*x2 - 12*x3 = 0; 2*x2 + 3*x3 => x2 = 0, x3 = 0, х1 - любой
Значит, собственный вектор (произвольный элемент выбирается любым, кроме как нулём) при L=0 равен (1 0 0) (предпочтительнее записывать в виде столбца, а не строки)
Найдем собственный вектор при L = -1 :
Система уравнений : -x1 + 19*x2 + 30*x3 = 0; -6*x2 - 12*x3 = 0; 2*x2 + 4*x3 = 0 => x2 = -2*x3; x1 = -8*x3; x3 - любой
Значит, собственный вектор при L=-1 равен (-8 -2 1)
Найдем собственный вектор при L = -3 :
Система уравнений : -3*x1 + 19*x2 + 30*x3 = 0; -4*x2 - 12*x3 = 0; 2*x2 + 6*x3 = 0 => x2 = -3*x3; x1 = -9*x3; x3 - любой
Значит, собственный вектор при L=-3 равен (-9 -3 1)
! -L 19 30 !
det ! 0 -7-L -12 ! = -L*((-7-L)*(3-L) + 2*12) = -L*(L^2+4*L+3) = -L*(L+3)*(L+1)
! 0 2 3-L!
Значит, собственные значения равны L1 = 0, L2 = -1, L3 = -3.
Найдём собственный вектор при L = 0 :
Система уравнений : 19*x2 + 30*x3 = 0; -7*x2 - 12*x3 = 0; 2*x2 + 3*x3 => x2 = 0, x3 = 0, х1 - любой
Значит, собственный вектор (произвольный элемент выбирается любым, кроме как нулём) при L=0 равен (1 0 0) (предпочтительнее записывать в виде столбца, а не строки)
Найдем собственный вектор при L = -1 :
Система уравнений : -x1 + 19*x2 + 30*x3 = 0; -6*x2 - 12*x3 = 0; 2*x2 + 4*x3 = 0 => x2 = -2*x3; x1 = -8*x3; x3 - любой
Значит, собственный вектор при L=-1 равен (-8 -2 1)
Найдем собственный вектор при L = -3 :
Система уравнений : -3*x1 + 19*x2 + 30*x3 = 0; -4*x2 - 12*x3 = 0; 2*x2 + 6*x3 = 0 => x2 = -3*x3; x1 = -9*x3; x3 - любой
Значит, собственный вектор при L=-3 равен (-9 -3 1)
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