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1
一、填空
1.
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
01
12
,
11
01
BA
,则
�AB
.
2. 设
D
为一个三阶行列式,第三列元素分别为-2,3,1,其余子式分别为 9,
6,
24,则
D =
_______.
3.
n
阶矩阵
A
可逆的充要条件是 _____ , 设 A
*
为
A 的伴随矩阵,则
1
A
-
=
______.
4. 若
n
阶矩阵满足
2
2 4 0A A E- - =
,
则
1
A
-
= __________.
5.
( )
1
2
1, 2,3, 4 _______,
3
4
æ ö
ç ÷
ç ÷
=
ç ÷
ç ÷
è ø
( )
1
2
1, 2,3, 4 _______
3
4
æ ö
ç ÷
ç ÷
=
ç ÷
ç ÷
è ø
.
6. 已知
,A B
为
n
阶矩阵,
2A =
,
3B = -
, 则
1T
A B
-
=
.
7. 设向量组
1 2 3
, ,
a a a
线性相关,则向量组
1 1 2 2 3 3
, , , , ,
a b a b a b
一定线性 .
8.
8. 设
A
三阶矩阵,若
A
=3,则
1
A
-
= ,
A
*
= .
9.
n
阶可逆矩阵
A
的列向量组为
1 2
, , ,
n
a a a
L
,则
{ }
1 2
, , ,
n
r
a a a
=L
.