.
. , , . 8. , , .
8
- | |||||
. , () , , . .
i , i;
xij i, , j Xj ;
Yi i, ( ).
i (i =1, 2, 3) :
(1)
( ) aij:
i, , j .
xi j = aijXj (7) :
(2)
= + Y, (3)
,
- .
Y - .
2.2.1.
( i): X1 = 600, X2 = 1000, X3 = 800 xij (i, j = 1, 2, 3):
, (1), Yi, i = 1, 2, 3, .
(4)
, Y = (90, 350, 100).
Y = (2000, 2000, 3000) (3), ,
= (-)-1 Y, (5)
.
S= (E-A)-1 .
2.2.2.
, , aij:
|
|
,
. (6)
2.2.3.
, ³ 0.
(5) Y, , . , , . , , ( - ) . , : , ( - ) .
(6) :
, , , (5) Y . , (5).
2.2.4. -
( - ):
(7)
2.2.5. ( - )- 1
, -1 , * -1 = ( ).
:
. (8)
(Bij) , B ij, B ij .
Bij= (-1) i+j Mij , (9)
M ij aij ( , , ).
( - ). - =
; ;
; ;
; ;
; ;
.
, .
2.2.6.
[ - ] ,
2.2.7. [ - ]
,
2.2.8. S
S=(E-A)-1=B-1=
.
2.2.9.
S Y, X :
= S× Y .
, Y = (2000, 2000, 3000)
X = (8637, 8322, 10985).
, .
. ().
. 9 ( Excel), . 10 ( Calc) . 11 ( ).
:
3.1.1. . 2:D5 .
|
|
3.1.2. B6:D8 :
6 =B3/A$3 7:B8;
9. . Excel
A | B | C | D | ||
- | |||||
- - | =3/$3 | =3/$4 | =D3/$5 | ||
= 4/$3 | =4/$4 | =D4/$5 | |||
= 5/$3 | =5/$4 | =D5/$5 | |||
=(B6:B8) | =(C6:C8) | =(D6:D8) | |||
=(B10>=1;C10>=1;D10>=1) | =(A11=;" ";" ") | ||||
- | =B12-B6 | =C12-C6 | =D12-D6 | ||
=B13-B7 | =C13-C7 | =D13-D7 | |||
=B14-B8 | =C14-C8 | =D14-D8 | |||
=(B15:D17) | =(B15:D17) | =(B15:D17) | |||
=(B15:D17) | =(B15:D17) | =(B15:D17) | |||
=(B15:D17) | =(B15:D17) | =(B15:D17) | |||
=(B18:D20;B21:B23) | |||||
=(B18:D20;B21:B23) | |||||
=(B18:D20;B21:B23) | |||||
6 =C3/A$4 7:8;
D6 =D3/A$5 D7:D8.
3.1.3. 10:D10 :
10 =(6:8) ( OpenOffice.org Calc =SUM(6:8));
10:D10.
3.1.4. 11 :
10. . Calc
A | B | C | D | ||
- | |||||
- - | =3/$3 | =3/$4 | =D3/$5 | ||
= 4/$3 | =4/$4 | =D4/$5 | |||
= 5/$3 | =5/$4 | =D5/$5 | |||
=SUM(B6:B8) | = SUM (C6:C8) | = SUM (D6:D8) | |||
=OR(B10>=1;C10>=1;D10>=1) | =IF(A11=;" ";" ") | ||||
- | =B12-B6 | =C12-C6 | =D12-D6 | ||
=B13-B7 | =C13-C7 | =D13-D7 | |||
=B14-B8 | =C14-C8 | =D14-D8 | |||
=MINVERSE(B15:D17) | = MINVERSE (B15:D17) | = MINVERSE (B15:D17) | |||
= MINVERSE (B15:D17) | = MINVERSE (B15:D17) | = MINVERSE (B15:D17) | |||
= MINVERSE (B15:D17) | = MINVERSE (B15:D17) | = MINVERSE (B15:D17) | |||
=MMULT(B18:D20;B21:B23) | |||||
= MMULT (B18:D20;B21:B23) | |||||
= MMULT (B18:D20;B21:B23) | |||||
11 =(10>=1;C10>=1;D10>=1) ( OpenOffice.org Calc =OR(B10>=1;C10>=1;D10>=1).
10:D10. (.. ), 11 . ;
|
|
C11
=(11=; ; ).
OpenOffice.org Calc
=IF(A11=; ; ).
11 , , .
3.1.5. 12 14 .
3.1.6. 15 17 -:
15 =12-6;
16:D17.
3.1.7. 18 20 , -:
18;
, 18:D20, ;
fx;
( OpenOffice.org Calc );
( OpenOffice.org Calc MINVERSE);
() ;
() -: 15:D17;
, Ctrl+Shift+Enter; 18:D20 =(15:D17) ( OpenOffice.org Calc =MINVERSE(15:D17)).
3.1.8. 21 23 :
21:23 (. 8);
D21:D23, , -, - ;
;
( Calc - ) ( Calc - MMULT);
1 () : 18:D20;
11. .
A | B | C | D | |
0,417 | 0,1 | 0,2 | ||
0,25 | 0,5 | |||
0,3 | 0,5 | |||
0,667 | 0,900 | 0,700 | ||
- | 0,583 | -0,1 | -0,2 | |
-0,25 | 0,5 | |||
-0,3 | 0,5 | |||
2,113 | 0,930 | 0,845 | ||
1,056 | 2,465 | 0,423 | ||
0,634 | 1,479 | 2,254 | ||
8619,72 | ||||
8309,86 | ||||
10985,92 |
2 ( Calc - ) - : 21:23;
, Ctrl+Shift+Enter. D21:D23 =(18:D20;B21:B23) ( OpenOffice.org Calc =MMULT(18:D20;21:23)).
|
|
, , . 12.
12. .
.
: [2], c. 509-515.
4.
.