. m´n, m- , n- , , . . , . aij, i- , j- .
=
. , . , :
. () , () .
cij = aij bij
= + = + .
() () .
a (+) =a a
(ab) = a b
. = ; B = , 2 + .
2 = , 2 + = .
: , :
A×B = C;
.
, , .
1) , .. ¹ . , = , .
, .
.
× = × =
, :
A×O = O; O×A = O,
.
2) , .. (), (), :
()=().
3) , .. (+) (+), :
( + ) = +
( + ) = + .
4) , a :
a(AB) = (aA)B = A(aB).
5) , :
() = ,
.
6) , det (AB) = detA×detB.
. = = .
= × = .
= × = 2×1 + 4×4 + 1×3 = 2 + 16 + 3 = 21.
|
|
. = , =
= × = = .
()
. = , :
det A = ,
1 , k . , , .. , .
, :
det A =
, , .. :
detA = , i = 1,2,,n.
, .
1.
1 a1k. , , . .
. aij , i- j- .
. =
= -5 + 18 + 6 = 19.
:. = , = . det (AB).
1- : det A = 4 6 = -2; det B = 15 2 = 13;
det (AB) = det A ×det B = -26.
2- : AB = ,
det (AB) = 7×18 - 8×19 = 126 152 = -26.
. , , , . s , s.
, , .
, .
. , (-1) , .
, , , , , , .
. s i1, ,is, , .
, .
. , :
XA = AX = E,
- , , -1.
, .
|
|
.
, :
AX = E Þ , i=(1,n), j=(1,n),
eij = 0, i ¹ j,
eij = 1, i = j.
, :
,
, .
. = , -1.
, -1= .
, , :
,
ji - ji .
. = , -1.
det A = 4 - 6 = -2.
M11=4; M12= 3; M21= 2; M22=1
x11= -2; x12= 1; x21= 3/2; x22= -1/2
, -1= .
. = , 3.
2 = = = ; A3 = = .
, .
. .
= -1
= -1(6 4) 1(9 1) + 2(12 2) = -2 8 + 20 = 10.
= = 2(0 2) 1(0 6) = 2.
= = 2(-4) 3(-6) = -8 + 18 = 10.
: -10 + 6 40 = -44.
. m´n r , , r+1 , , .. r m n.
, , .
, .
. Rg .
. .
~ ~ , RgA = 2.
: .
~ ~ ~ , Rg = 2.
. .
~ , Þ Rg = 2.