3.1. . .
- .
: :
1 2 3
200 100 150
350 200 180
400 250 260
() :
, .
:
.
, , , .
m, n. m x n.
m=n, . a11, a22,amn , am1 a1n .
, . :
() , m n , , () .
;
k , k.
.
i= 1,2,3, m
J= 1,2,3 n
aij
, ij i- j- .
:
, . det(A).
(m=n=2) .
.
.
1) , .
2) , (), .
3) .
4) k=0, .
3.2. .
-
:
;
1) , .
2) 0, .
( ). . :
|
|
- .
- .
- .
.
:
:
~
3, , , 3
~ ~ ~
2, 3, , 2
~ ~ ~
3, 8.
~ ~
.
: 1=1; 2=2; 3=3
4.
.
n m : S
, , , , , : , .
, | |||||
P1 | P2 | Pn | |||
S1 | 1 | a11 | 12 | a1n | |
S2 | 2 | a21 | a22 | a2n | |
Sm | m | am1 | am2 | amn | |
1 | 2 | n |
1 1
2- . 2 .. n n
11 . 1
nn . n
, Z
: , .
. S.
m S i(i=1,,m) n
- . - | 1 .() | ||||
1 | 2 | n | |||
S1 | 1 | a11 | 12 | a1n | |
S2 | 2 | a21 | a22 | a2n | |
Sm | m | am1 | am2 | amn | |
1 . | 1 | 2 | n |
, .
1, 2n 1, 2n
11 1, 1
nn n, n
Z .
: , - , .
Z,
Z- , 1, 2n, .
1, 2n .
|
|
1. . .
, | |||
P1 | P2 | ||
S1 | 20 | ||
S2 | 40 | ||
S3 | |||
() |
, , .. Z max.
1, 2 - 1, 2,
Z=50x1+40x2 ()
1, 2, Z max
|
|
1 | ||
2 |
L1:
1 | ||
2 |
L2:
1 | ||
2 |
L3:
D Z = 501+402
Z=0, 501+402=0
2=
1 | ||
2 | -5 |
2=
ON 501+402=Z (50;40) 10(5;4).
501+402=0 N , L2, L3, .
:
1 2
, max 1 1
2 2
2. .
1 | |||
1 | 2 | ||
S1 | 9 | ||
S2 | 8 | ||
S3 | |||
1 |
1, 2 1, 2 Zmin=41+62
1 | ||
2 |
L1
1 | ||
2 |
L2
1 | ||
2 |
L3
ABC -
1 | ||
2 | -2 |
N 4 x1 +6 x2 =Z. Z JN , .
, L1 L2.
1=2 2=3
.. 2. 1; 3. 2, .