- 2 , .
- , 0.
- , .
- .
- det(AB)=detA*debt( )
- , i≠j.
9.
-1 , -1=-1=→ .
0
: , -1.
:
[nxn]= det(a)=0 S= A-1=1/Δn*S
AA-1=E
A(1/Δn*S)=E
(1/Δn)* * =(1/Δn)* = =(1/Δn)* =
:
, 2 ..
A-1
-1=-1=
BA=AB=E (1-2)
-1-BA= -1-AB=E-E
A(A-1-B)=A(A-1-B)=0
A-1-B=0 => (a-1)ij=bij => A-1=B.
10.
A-1|AX=→ EX=A-1B→ X=A-1B
A , X .
11.
n
X=A-1B= =
12.
.
, Δi- .
.
n n , 0, , .
13.
- k k , , k- . 0
- S1, S2Sn , n1, n2nn n1S1+n2S2++nnSn=0 ni≠0. =0, . .
14.
-
m n , , :
- rA=rÂ=n 1 .
- rA=rÂ<n - ∞ .
- rA≠rÂ≤n - .
16.
, 1 .
, .
1. 1 (- = n-rA)
2. .
,
- ai1≠0
- S1→S1:a11
- Si→Si-ai1S1, i=2,3...m
- aj2≠0(j≠1) .. aj2=0 j=2m, aj3≠0 (j≠1).
18.
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