. Z , , :
) ( ), -
,
+ ;
) ( ),
α Z,
α α ;
) , , α β
():
1. + = +
2. ( + ) + = + ( + )
3. , + 0 =
4. , + (- )= .
5. α( + ) = α + α .
6. (α + β) = α + β .
7. α (β ) =(α β) .
8. 1 = .
:
1. .
2. , .
3. ()
= (x1, x2, , xn), :
+ = (x1, x2, xn) + (y1, y2, yn), = (x1+y1, x2+y2, xn+yn).
α = α (x1, x2, xn) = (αx1, αx2, αxn).
Rn.
. ( 1, 2, m) , α1, α2, αm, , α1 1+α2 2+ + αm n = 0.
. ( 1, 2, m) , α1 1+α2 2+ + αm m = α1 = α2 = αm = 0.
. , 1, 2, 3
= α1 1+α2 2+ + αs s, 1, 2, s
. 1, 2, m , .
Rn:
1 =( 11, 12, 1n),, m =( m1, m2, mm). ,
m . :
α1 (x11, x12, x1n) + α2 (x21, x22, x2n) + + αm (xm1, xm2, xmn) = (0; 0; 0...0). :
α1 = α2 = αm = 0, .
. |
, . .
|
|
1=(1;2;3;4;1), 2=(2;-1;1;2;3), 3=(3;1;4;6;4)
: α1(1;2;3;4;1) + α2(2;-1;1;2;3) + α3(3;1;4;6;4) = (0;0;0;0;0)
. , .
m 1 =( 11, 12, 1n),
2 =( 21, 22, 2n), m =( m1, m2, mm).
. , :
1) ;
2) .
:
, .
:
1. , ;
2. ;
3. ;
4. .
2-4 , . , , .
1-3 "" "", .
18.1 . , , -- , -- . 15.3 - . . , . , . , . , , -- .
: :