(). , , .
:
a11 x1 | + | a12 x2 | + | ... | + | a1n xn | = | a1,n+1 | |
a21 x1 | + | a22 x2 | + | ... | + | a2n xn | = | a2,n+1 | (4.1) |
.... | . | .... | . | ... | . | .... | . | .... | |
an1 x1 | + | an2 x2 | + | ... | + | ann xn | = | an,n+1 |
aij - (i=1,...,n, j=1,...,n+1);
xi - () ;
n - .
(4.1) n n+1:
a11 | a12 | ... | a1n | a1,n+1 |
a21 | a22 | ... | a2n | a2,n+1 |
. | . | . | . | . |
an1 | an2 | ... | ann | an,n+1 |
n , (4.1).
- xi, (4.1) .
xi (4.1) xi= D i /D, D - , D i - , i- .
2-, 3- , , , , .
4.2.
. , , , . ; .
3-
a 11 x 1 | + | a 12 x 2 | + | a 13 x 3 | = | a 14 | |
a 21 x 1 | + | a 22 x 2 | + | a 23 x 3 | = | a 24 | (4.1) |
a 31 x 1 | + | a 32 x 2 | + | a 33 x 3 | = | a 34 | . |
(4.1) x 1:
x 1 = (a 14 - a 12 x 2 - a 13 x 3) / a 11 , | (4.2) |
:
x 1 + ![]() ![]() ![]() | (4.3) |
![]() | (4.4) |
(4.2) (4.4) (4.1) :
x 1 | + | ![]() | + | ![]() | = | ![]() | |
![]() | + | ![]() | = | ![]() | (4.5) | ||
![]() | + | ![]() | = | ![]() | , |
= a ij - a i1 .
, i=2,3; j = 2,3,4,
|
|
.. x 1.
(4.5) x 2 :
x 2 = (![]() ![]() ![]() | (4.6) |
:
x 2 + ![]() ![]() | (4.7) |
![]() ![]() ![]() | (4.8) |
(4.6) (4.8) (4.5) :
x 1 | + | ![]() | + | ![]() | = | ![]() | |
x 2 | + | ![]() | = | ![]() | (4.9) | ||
![]() | = | ![]() | , |
=
-
.
, j = 3,4,
.. x 2.
(4.9) x 3: x 3 = /
,
x 3 = .
:
x 1 | + | ![]() | + | ![]() | = | ![]() | |
x 2 | + | ![]() | = | ![]() | (4.10) | ||
x 3 | = | ![]() | . |
. :
![]() | ![]() | ||
![]() | (4.11) | ||
. |
. , .
. (4.10) x 3
![]() | (4.12) |
(4.10), :
![]() | (4.13) |
x 2, x 3 (4.10), x 1:
![]() | (4.14) |
(4.12), (4.13), (4.14) (4.1).
n- . k- (k=1,2,3,...,n) :
![]() | j = 1,2,...,n+1, | (4.15) |
![]() | i = k+1,...,n; j = 1,2,...,n+1. | (4.16) |
, .. k=n, (4.15), (4.16) i.
(4.15) a kk. , . , k- n- , a kk . , , , a kk , k- . . - , , D . , , .. , .