n- , k, =kA.
, , 0 = 0 . .
A1, A2,..., n, k 1, k 2,..., kn,
B=k1A1+ k2A2++ knAn,
. . j- j = 1, 2,..., n , , j- A1, A2,..., n k 1, k 2,..., kn.
1. A1, A2,..., r (r³2) , , .
. = (8; 5; 11), A1 = (1; 2; 3), A2 = (3; 2; 1), = (3; 1; 2) , - 1, A2 , = 21 - 2 + 3.
2. A1, A2,..., r (r³2) , k1, k2,..., kr ,
k1A1+ k2A2++ krAr=0.
, kj =0 (j = 1, 2,..., r), .
. A1 = (2; 4; 3), 2 = (2; 3; 1), = (5; 3; 2),4 = (1; 7; 3) , A1 + 2A2 - - 4 = 0, .
. A1, A2,..., s (s<r) A1, A2,...,r (r³2) , .
.
A1, A2,..., s ; k1A1+ k2A2++ ksAs=0, . r - s ,
k1A1+ k2A2++ ksAs+ 0 .As+1++0 .Ar=0
. . A1, A2,...,r (r³2) .¨
, , , , . -: A1, A2,...,r (r³2) , .
. A1, A2,...,n. , . .
( ).
. , 1 k¹0 n, n=An+kA1,
|
|
A1, A2,...,n-1,An .
, .
, A1, A2,...,r (r³2), , . . , , .
(*)
, ; , , .
, A1, A2,...,m. .
. (*) , .
( ).
, . .
. n + 1 n- .
( )