a b S ℄ d X ` W V Z e Y \ \ _
( A ) ( 2011.11.18 )
? 16 G F8 ? = '
(30
U
)
A J
A(1, 2, 3), B(2, 1, 4, ), C(1, 3, 5), D(3, 2, 1).
+
1. B, C
6 G L 9
L
Æ
A, B, C
6 G ( %
Π
Æ
2. △ABC
Æ %
S
∠ABC
4 % 7
ABCD
Æ 7
V
3. A
L
Æ "
D
Π
Æ " L 9
AB
D
CD
K Æ "
4.
A, B, C, D
Æ * % Æ
A, B, C
Æ E Æ
5.
L 9
AB
.
CD
> Q P 6 , % Æ N , % Æ ! :
T
(20
U
)
1.
a, b
- M 2 9 < R
ax
1
+ bx
2
+ 2x
3
= 1
(b − 1)x
2
+ x
3
= 0
ax
1
+ bx
2
+ (1 − b)x
3
= 3 − 2b
B + ) 6 B
2.
0
A =
1 −1 0 0
0 1 −1 0
0 0 1 −1
0 0 0 1
, B =
2 1 3 4
0 2 1 3
0 0 2 1
0 0 0 2
,
H
X(I − B
−1
A)
T
B
T
= I.
[
(30
U
)
0
A = (a
ij
)
m×n
, B = (b
ij
)
n×m
.
/
D
1
= det(I
m
− AB), D
2
= det(I
n
− BA),
r
1
= r(I
m
− AB)
r
2
= r(I
n
− BA)
A J
1.
+
D
1
D
D
2
det
I
m
A
B I
n
!
K 8
r
1
D
r
2
r
I
m
A
B I
n
!
K 8 +
1 0 ... 0 a
1
0 1 ... 0 a
2
... ... ... ... ...
0 0 ... 1 a
m
b
1
b
2
... b
m
1
1 − a
1
b
1
−a
1
b
2
... −a
1
b
m
−a
2
b
1
1 − a
2
b
2
... −a
2
b
m
... ... ... ...
−a
m
b
1
−a
m
b
2
... 1 − a
m
b
m
Æ O ; # 3
2.
I &
m = n
2
det(AB) = det(A)det(B);
+
det
a b c d
−b a d −c
−c −d a b
−d c −b a
;
m 6= n
2 C
det(AB)
Æ $ I & K
1