线性代数习题.docx

文档介绍：第一章 行列式
4
1
2
4
2
1
4
1
/八 1
2
0
2 ；
/c、 3
1
2
1
1)
(2)
10
5
2
0
1
2
3
2
0
1
1
7
5
0
6
2
:
ab ac ae
(3) bd cd de
bf cf ef
a
1
0
0
/、 1
b
1
0
4)门
0
1
c
1
0
0
1
d
(1)
10
1
4
2
1
10
5
1
0
10
10
10
14
1)43
10
14
10
14
C2 03
9
0
17
9
0
17
10
2 =0
14
1 4 1
2 14 0
2
1 2 1
C4 C2
3 1 2 2
r4 r2
3
2 3 2
12 3 0
1
0 6 2
5 0 6 2
2
2
3
1
5
4 0
1 2 2
3 0
1 4 0
2140
4 A 3 1 2 2
12 3 0
0 0 0 0
ab
ac
ae
b
c
e
1
1
1
⑶
bd
cd
de
=adf
b
c
e
=adfbce
1
1
1
=4abcdef
bf
cf
ef
b
c
e
1
1
1
证明
a
1
0
0
1 0 0
b 1 0 ri ar2
1 c 1 ~~
0 1 d
C3 de?
1 ab
0 1 ab
1 b
0 1
0 0
a
1
c
1
=(
1)( 1)21
1 ab
1
0
a ad
3 2 1
c 1 cd =( 1)( 1)
1 0
ab
1
ad
1 cd
= abcd
ab cd
2 a
ab
b2
ax
by
ay
bz
az
bx
= (a3
(1)
2a
a b
2b
=(a b)3;
(2)
ay
bz
az
bx
ax
by
1
1
1
az
bx
ax
by
ay
bz
:
2 a
x y z
3
b ) y z x
z x y
ad 1
b2
2
c
d2
a
2 a
4 a
(a 1)2 (b 1)2 (c 1)2 (d 1)2
(a
(b
(c
(d
1 1 1
b c d
2 2 2
b c d
4 4 4
b c d
x 1 0
0 x 1
(5)
0 0 0
an an 1 an 2
(1)左边
c3 c1
2a
1
2)2 (a 3)2
2)2 (b 3)2
2)2 (c 3)2
2)2 (d 3)2
(a
0；
b)(a c)(a d)(b c)(b
0
0
0
0
n n 1
x a1x
x
1
a2
x a1
ab a2
b a
0
.2 2
b a
2b 2a
0
1)31
ab
d) (c d)(a b c
an 1 x an .
b2
2b
2 a
2a
(b a)(b
d)；
、a b a a)1 2
(a b)3右边
⑵左边
按第一列
分开
x ay bz az a y az bx ax
z ax by ay
bx
by
bz
y ay bz az bx
b z az bx ax by
x ax by ay bz
x
y
z
x
y
z
a3
y
z
x
b3
y
z
x
(1)2
z
x
y
z
x
y
a2 1 4a 4 6a 9
b2 1 4b 4 6b 9
2
c 1 4c 4 6c 9
d2 1 4d 4 6d 9
分别再分 2
x ay