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l ( ) . :
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2
1. f (x) :
f (A).
2.
:
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1) ;
2) ;
3) .
3. : :
, .
:
1) ;
2) ;
3) φ ;
4) ;
5) , ;
6) , .
4. ABCD:
:
1) AB;
2) ABC;
3) ABC BCD;
4) AB;
5) DK, D;
6) DK ABC;
7) AB BC;
8) AD ABC;
9) .
1
: , , . . 3- .
A 2. A " " ( (23)):
A 2 = A A =
2 , ( (21)):
E =
f (A), ( (22)):
|
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:
2
1) :
, AX = B,
( 3, . . 23 = 0).
2) . (29) :
, (25):
∆ ≠ 0, .
(30):
3) .
a) , .
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2- (24).
(. (31)):
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;
2) , :
;
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.
3
1) (35):
.
2) , (38) (39):
3) (41):
.
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,
4) (42):
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(47): .
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2) :
3) :
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4
1) (36):
2) ABC, , ABC, . . , . . , , (37):
= {3(2); 21; 11} = {1; 1; 2},
= {7; 3; 3}.
(43):
ABC , , , = {9; 17; 4}. , ( (48): ABC.
|
|
3) , ABC BCD, BCD, , ( (49):
BCD.
BCD , : ={3; 7; 4}.
() ABC BCD
(50):
.
4) AB , A (2; 1; 1) = {1; 1; 2} ( (51)):
AB.
: , ( (53)):
, t, :
AB.
5) DK , D ABC. , ABC. , , = = {9; 17; 4}. DK, D (1; 0; 3)
= {9; 17; 4} ( (52)):
DK.
6) , DK ABC, DK.
t, :
DK.
DK ABC ( ) , , , , . . ABC. K , :
t:
K, :
, DK ABC: .
7) AB BC , -
AB BC: = {1; 1; 2}
= {8; 4; 1}.
(54):
AB BC:
8) AD ABC, : = {1; 1; 4}. ABC = {9; 17; 4}. ABC (55):
AD ABC:
9) (. 19).
:
1)
2) :
3) ;
4)
5) DK: ;
6) ;
7) ;
8) ;
9) . 19.
1 -
1 5 , " ". 2 4 " . ".
, .
; , , . . , (. ).
1
1. .
(2; 3), (2; 7), (6; 1) | (3; 3), (4; 1), (2; 5) | ||
(5; 1), (6; 3), (4; 7) | (3; 5), (2; 2), (2; 4) | ||
(4; 5), (3; 2), (5; 4) | (2; 4), (5; 6), (3; 4) | ||
(7; 7), (1; 2), (5; 4) | (3; 7), (4; 1), (2; 5) | ||
(3; 4), (4; 5), (8; 3) | (4; 3), (3; 2), (7; 2) |
:
|
|
1) ;
2) ;
3) ;
4) , ;
5) ( );
6) .
2. , l λ.
l | λ | l | λ | ||||
(1; 0) | y + 2 = 0 | 1: 1 | (5; 1) | x + 1 = 0 | 1: 1 | ||
(3; 1) | 3 x = 16 | 3: 4 | (5; 4) | 5 x = 1 | 5: 1 | ||
(3; 0) | x = 0 | 2: 1 | (1; 0) | 2 x = 7 | 2: 3 | ||
(2; 0) | 4 x = 1 | 4: 3 | (1; 2) | x = 4 | 1: 2 | ||
(0; 0) | 2 x + 5 = 0 | 2: 3 | (3; 2) | 3 x = 1 | 3: 1 |
, , l λ. .
3. 2- .
7 x 2 9 y 2 + 42 x + 18 y 9 = 0 | 9 x 2 + 4 y 2 54 x + 8 y + 49 = 0 | ||
x 2 + 2 x 12 y + 37 = 0 | x 2 10 x + 4 y + 17 = 0 | ||
5 x 2 + 9 y 2 + 10 x 54 y + 41 = 0 | 3 x 2 y 2 30 x 2 y + 62 = 0 | ||
y 2 + 6 x + 6 y 3 = 0 | y 2 8 x 4 y 4 = 0 | ||
5 x 2 4 y 2 20 x 24 y 36 = 0 | 7 x 2 + 16 y 2 56 x + 64 y + 64 = 0 |
. , . .
4. 2- .
x 2 + 2 y 2 2 x + 8 y + 3 = 0 | x + 2 y + 3 = 0 | |
x 2 2 y 2 + 4 x + 4 y 6 = 0 | x + 2 y = 0 | |
x 2 + 6 x 16 y + 25 = 0 | x 4 y + 15 = 0 | |
x 2 + 4 y 2 6 x + 8 y + 5 = 0 | x 2 y 5 = 0 | |
y 2 4 x 6 y 15 = 0 | 2 x + y 3 = 0 | |
x 2 5 y 2 + 10 x + 20 y 15 = 0 | x 5 y + 15 = 0 | |
x 2 + 4 y 2 + 2 x 32 y + 45 = 0 | x y + 5 = 0 | |
x 2 4 x + 8 y + 44 = 0 | x 2 y 20 = 0 | |
2 x 2 y 2 16 x 6 y + 19 = 0 | x y 7 = 0 | |
y 2 + 10 x + 8 y 34 = 0 | 2 x + y + 4 = 0 |
:
1) 2- ;
2) ;
3) .
5. ().
:
1) ;
2) , , ;
3) (), , ;
4) .
|
|
2
1. f (x) .
f (x) | ||
f (x) | ||
.
2.
.
:
1) ;
2) ;
3) .
3. .
:
1) ;
2) ;
3) φ ;
4) ;
5) , ;
6) , .
4. ABCD.
(1; 2; 1), (0; 0; 1), (1; 3; 3), D (2; 1; 1) | |
(7; 2; 4), (7; 1; 2), (3; 3; 1), D (4; 2; 1) | |
(1; 3; 6), (2; 2; 1), (1; 0; 1), D (4; 6; 3) | |
(2; 0; 4), (1; 7; 1), (4; 8; 4), D (1; 4; 6) | |
(1; 2; 0), (3; 0; 1), (5; 2; 3), D (3; 2; 1) | |
(1; 1; 2), (2; 1; 2), (2; 0; 4), D (2; 1; 2) | |
(4; 2; 5), (2; 3; 0), (10; 5; 8), D (5; 2; 4) | |
(2; 1; 1), (1; 3; 2), (2; 3; 1), D (1; 2; 3) | |
(1; 1; 2), (2; 0; 3), (3; 6; 3), D (1; 2; 7) | |
(4; 1; 3), (2; 1; 0), (0; 5; 1), D (2; 1; 1) |
:
1) AB;
2) ABC;
3) ABC BCD;
4) AB;
5) DK, D;
6) DK ABC;
7) AB BC;
8) AD ABC;
9) .
1. , .. . 2 . . 1 / .. . .: -, 2003. 288 .
2. , .. : / .. . .: . ., 1998. 479 .
3. , .. . 2 . . 1
/ .. , .. , .. . .: . ., 1999. 304 .
4. , .. / .. . .: . ., 2001. 304 .
005-93, . 2; 95 3004 ,
. 183010 , , 13.
14.09.2007. 18.09.2007. 60´841/16.
. . . . . 2,79. .-. . 2,18. 443. 300 .