1
.
1.. , m n :
a ij, i= 1, m, j=1, n, . (m,n) () . :
(m,n) , (m,n). , m=n, . m=n .
A+B A, B ϵ C ϵ ,
:
Cij = Aij +Bij, i = 1, m, j =1, n.
λ A ϵ λ
B ϵ , λ:
A ϵ λ
B ϵ , λ:
ϵ (m,n) B ϵ M (n,k) C ϵ , Cij i- j- :
Cij=
=() :
B | C | |
A | AB | X |
(det A≠0), = = ,
, , :
= det ;
ij a ij ;
ij , ;
, *; * . = *, .
2. . n n :
, . = ,
(1) =.
1. . (1) = det 0,
t , i- .
2. . (2) , = , = , = .
3. . (1),
(1). (1`)
(1)
, .
1.1. M,N,P , . :
|
|
( )
?
, :
()
, , :
()
1.2. - , :
) 1 10 1 15 2;
) 2 20 3;
) 3 100 5.
p q , ( ) :
()
: , :
()
p q
()
.. p 1, 2 , 3 170, 200,500 , q 450,2000,5000 .
1.3. , ( )
()
(1), (2) (3) i :
1=10, 2 =2, 3= 8, 4 =4
, i
Y = AX,
Y= () - ;