, (.. ):
(1)
, (1), = (ij), , Δ = det(A) .
. (1) , , .
(2)
Δ j , Δ j- (1).
. , , (2), (1). i- , Δ j j- :
(.. , bk) Δ, k=i, 0, k≠j. i- bi Δ. , i- (2) , .. . , (2) (1).
(2), , 1, 2,, n , :
(3)
. : 1 11, 2 21 .. . :
(a 11 A 11 +a 21 A 21 ++an 1 An 1) c 1 + (a 12 A 11 +a 22 A 21 ++an 2 An 1) c 2 +
+ (a 1 n A 11 +a 2 n A 21 ++annAn 1 ) cn=b 1 A 11 +b 2 A 2 1 ++bnAn 1.
Δ, 0. Δ1 . ,
Δ 1 = Δ1.
, 12, 22, , n 2,
Δ 2 = Δ2
Δ n = Δ n. Δ≠0,
, (1) , . .
, , , . n- . , , - , .
.
|
|
cj Δ = Δ j, j =1,2,, n
:
Δ=0, Δ1, Δ2,, Δ n 0, (1) ; Δ=Δ1=Δ2==Δ n =0 (1) , .
: n n , 0.