L.
6
C , " ÎL C = + . C = + .
, :R2R2 , " = [ 1, 2]ÎR2 = [ 1+ 2, 2 2], :R2R2 , " = [ 1, 2] = [3 1, 1 2 2], C = + , " = [ 1, 2]ÎR2
C = + = [ 1+ 2, 2 2] + [3 1, 1 2 2] = [4 1+ 2, 1].
6, , :
C ( + ) = ( + ) + ( + ) = + + + =
= ( + ) + ( + ) = C + C ,
C (a ) = (a ) + (a ) = a( ) +a( D) = a( + ) = a C .
C = + .
L . ÎL. :
;
A= ;
B = ;
C = C C .
= , = , = .
, C = + , :
C = ( + ) = + ,
,
= + = + = ( + ),
= = ( + ), = + . , .
7
a C, C = a( ). C = a .
, : R2R2 , " = [ 1, 2]ÎR2 = [ 1+ 2, 2 2], ()
= 3( ) = 3[ 1+ 2, 2 2] = [3 1+3 2, 6 2].
, :
1) , a .
2) C = a = a, .
, :
( ) = ( +( )) = .
, , .
8
() C, C = ( ). C = .
, .
, :R2R2 , " =[ 1, 2]ÎR2 = [ 1+ 2, 2 2], :R2R2, " = [ 1, 2]ÎR2 = [3 1, 1 2 2], C = . = [ 1, 2]ÎR2
C = ( ) = ([3 1, 1 2 2]) = [3 1 + ( 1 2 2), 2( 1 2 2)] =
= [ 4 x 1 2 x 2, 2 x 1 4 x 2].
|
|
, , , .
, , C1 = :
C1 = ( ) = ([ 1+ 2, 2 2]) = [3( 1 + 1), 1+ 2 2(2 2)] =
= [ 3 x 1 +3 x 2, x 1 3 x 2].
, C ≠ C1 .
, - , :
2 = ( ), 3 = ( ( )), ..
, , .
L . C = . :
L ,
,
Z ( ).
= , Z = , Z = .
Z = = () = () Z = ,
, =..
, -.
( ) , , .
.
4
ÎV2 ( + ) (. ) , , 180 . - .
, (, ) . ( 1)
= (, ), = ( , ).
C = + = . .
C = ( + ) = (, ) + ( , ) = (0,2 ),
= (. ) = ( ) = (( ), ( )) = ( , )
|
, .
= (1, 0) Þ , , C = ( + ) = (0, 0),
=(. ) = (1, 0),
= (0, 1) Þ = (0, 1), = (0, 1), C = ( + ) = (0, 2),
= (. ) = (0, 1).
,
= , = ,
= ( +), D = ( ).
, C = + .
.
9
1 , , L.
,
. 1 = 1. = .
, 1 1.
, , .
, 1 , .., 9,
1( + ) = 1() = = 1()+ 1(),
1(l ) = 1() = =l 1().
, .
, , , , :
+ = + , +( + C) = ( + ) + C;
, :
|
|
C ( ) = (C ) , ≠ .
, .
( l) =
l , . ( l) ,
| l | = 0 = 0
.
, | A l | l. , () .
, , , , .
, , , , . , , . . .
10
L n , :L n L n . , l , ..
= l ,
l . l , .
, . , ( ), - ¹ 0 ( ), , l , = l.
, , l , .. = l , ¹ 0. = , = l
= l Þ l = , ( l) = .
= , l = ,
( l) =
(*)
-, , , , .. .
, l ( ) , .. ().
, l0 , .. l0 . l = l0 (*) , , . (*) , , = , , = l0 , .. , l0.
, , , .
-, - . , .
|
|
:
1. .
2. .
3. ,
, ..
, . , , .
4. (7.1)
, l l i, i = . i = i = , l i.
5. 4 .
, l i (7. 1) , , l i.
6
, = .
1 2 . . :
= = (1l)(1+l) 3 = (1l2) 3 = l2 4,
l2 4 = 0 Þ l1 = 2, l2 = 2.
, , .
(7.1): .
, , 1, , , , 1 = 3 2. 2 = t, x 1 = 3 t, 1 = (3 t, t) .
1, 1 + 2 = 0, 1 = 2. , , 2 = ( s, s), l1 = 2.
, 1 = (3 t, t), l1 = 2 2 = ( s, s), l1 = 2.