9.3. , λ, : = λ , , , λ. λ .
(9.3) x`j = λxj, :
.
. (9.5)
, 0 ( ). :
λ, . :
| A - λE | = 0, (9.6)
-λ. λ | A - λE | .
:
1) . . (. (9.4)), , . , . , | A-λE | .
2) (.. ij=aji), (9.6) .
:
1) 1, 2, 3, λ1, λ2, λ3 , :
(9.7) .
2) , .
3) , .
.
: (1- λ)(5 - λ)(1 - λ) + 6 - 9(5 - λ) - (1 - λ) - (1 - λ) = 0, λ ³ - 7 λ ² + 36 = 0, λ 1 = -2, λ 2 = 3, λ 3 = 6.
, λ. (9.5) , (1) ={ x1,x2,x3 } , λ 1=-2,
- , . (1) ={ a,0,- a }, . , , | x (1) |=1, (1) =
(9.5) λ 2=3, - x (2) ={ y1,y2,y3 }:
, (2) ={ b,-b,b } , | x (2) |=1, x (2) =
λ 3 = 6 x (3) ={ z1, z2, z3 }:
|
|
, x (3) ={ c, 2c,c }
(3) = , (1) (2) = ab ab = 0, x (1) x (3) = ac ac = 0, x (2) x (3) = bc - 2 bc + bc = 0. , .
10.
. . .
10.1. 1, 2,,n , .
:
(n = 2),
(n = 3). (10.1)
:
10.2. , , , .
:
1) .
( n = 2).
: . :
(10.2) :
, .
2) .
( n = 2).
:
, :
. :
(10.2) , : , .
. , 9, , .
10.3. (10.1) . (10.3)
, , . , (10.3) . , .