09-10 (A )
4 28
1 1
1
1. A n , A , det A , det A 15 A _
4
3
2. 1 , 2 2 , A (2 1 2 , 1 2 ) , B (1 , 2 ) .
A 6 , B _
3.
r (1 , 2 , s , ) r (1 , 2 , s ) k ,
r (1 , 2 , s , ) k 1,
r (1 , 2 , s , , ) = _
4. A 5 , r ( A) 4 , A x 0 A A
*
*
_
5. A (aij )
2007
4 28
1 A * n A A 2 2A*
.
22n-1
|2A * |=2n|A *|=2n|A|n-1 2n 2n1 22n-1
2 4 A B A B r ( A) 3
r ( B) 4 r ( A* B* )
.
1.
r A* 1r B* 4B*
r A* B* r A* 1.
3 n ( x,0, ,0, x)T x 0 A E T
1
.
A1 E T x =
x
-1 T 2 x 2
1
1
1
AA-1 E - T E T E - T T - T T
x
2005 A
4 28
1 1 2 2
1 1 , 2 , 1 , 2 , 3 1 2 1 2 2
1 2
1 2
2
16
O C
C,D A A-1=
D O
2 A
O
A 1
C
1
D 1
O
3 A
A E A 2E 2 A 3E 0, 2 A* 3E
0
2
2
4 f ( x1, x2 , x3 ) x12 2 x2 4 x3 2 x1x2 2tx1x3 t
t 2
5 A,B,C n ABC=E|2CAB|=
2n
6
n 1 , 2 , 3 , 4