x , - n - . :
= ; = ;
, i - j - (aij). - , .
( ).
, - . :
[a11 12... 1n]. : [2 9 7 4 5 3]. 16.
, , - . :
: 61.
. .
, , i j aij=bij.
, (m = n), .
, , ,
, .
11, 22,..., nn , 1n, 2n-1,..., n1- .
:
1. - , , , , . .
:
2. - , , ..
3. - , , , ..
:
4. - , ,
,
:
, , (11, 22,..., nn) , i,j=1,2,..., n aij=aji .
.
: , .
.
= [ij] = [bij] =[cij] , ; .. cij=aij +bij.
+ = + =
:
= = + =
λ λ , λ:
λ∙= λ∙ =
: 1) λ = 2
= 2 =
2) λ = 2
|
|
= 2 =
(-1)∙ , -.
:
1. + = +( ).
2. ( + ) + = + ( + ) ().
3. +0 = .
4. + (-)=0.
5. 1=.
6. λ(μ) = (λμ) ( ).
7. λ(+) =λ+ λ ( ).
8. (λ+μ) = λ+ μ( ).
(, , , 0 - λ,μ R)
- : + (-).
.
, . :
4x2 = , 2x4 = , 3x4= .
, . , . , . , 2, 3. , 3 , 4 . , 3 , 2 . , 3 , 4 .
- , .
m×n=(aij) Bn×k=(bij) Cm×k=(cij) , cij= = ai1b1j +ai2b2j ai3b3j + +aipbpj .
, , i- j- i- j- .
. , , , , ≠ . =·, .
:
1) ,
A3×2= B2×5= .
: 32, 25, 35
A3×2B2×5= =
= =
2) ·,
A= , B=
:
AB= =
BA= =
, , ≠ .
,
=ŷ=, 0=0=0
.
, , , 0, :
1) (+) = + 4) 0 = 0
2) (+) = + · 5) 0 = 0
3) () = (·) 6) =
7) ŷ =
n ( > 1) , . ,
|
|
n =
n , .
0 ( ≠ 0) , , 0 = .
1 , 1 = .
q p+q , pq = p+q (()q= pq).
, . , ´ . ,
A = , AT = .
A= = , i=1,2,....n; j=1,2,...,m.
: = , =
:
1) (λ) =λ, λ R.
2) ( + ) = + .
3) () = .
4) ( ∙) = .
5) - , = .
6) () () .
7) X - n - n×1,
T X = X12 + 22 +... + n2, X =
.
1. +2,
A = B = . :
2. -·:
= = :
3. :
3.1 :
3.2 :
4. ƒ () :
4.1.ƒ ()=x2-3+1, = :
4.2. ƒ () = 2-2+5, = :
5. ∙ ∙ :
5.1. = :
5.2. = :
?
: , ,