线性代数第一章习题
题型一：题型一：求逆序数
113L2
12
2
2L2
题型二：题型二：求系数或常数项
5x1221xx133
2设行列式D
x23213x
，则D的展开式中，x4的系数为___x3的系数为___
x10x223x3多项式fx中的常数项是（）710431
A3
71
C
x
15D15
B3
题型三：题型三：求fx根的个数根的个数
x24记行列式x13x24x3x24x55x7x3为fx则方程fx0的根的个数为（）3x54x32x22x12x22x33x34x
2A1BC3D4题型四：题型四：求元素值由比较复杂的数字构成的行列式
321533205357228472184
103100204199200395301300600
f题型五：题型五：求特殊行列式的值1aa0011aa0D5011aa00100a1100
000

1aa11a
LL
0
000Ma
1a

11a1a2011a2D
MMM000000011L1101L1110L1D
MMMOM111L000D
M
0L0OML1a
1
L

1
111M1
111L100L00100L0200MOMMMM

10L000000L000
题型六：题型六：求代数余子式
31125134D，求A313A322A332A342011153311D
1M1320M0503M0L2
1L0L0求A11A12LA1
OML

f题型七：题型七：根据已知行列式的值求解另一行列式的值
a1如果a2a3
b1b2b3
c1
a13b1
b12c1b22c2b32c3
c1a1c2a2_____c3a3
c2m则a23b2c3a33b3
题型八：题型八：Va
dermo
de行列式
求解下列方程1xx
2
1aa
2
1bb1
2
1cc2c31x21xx2
2xx222322333
0
x3
a3
b3
1x31xx3
2xx3
1x41
2x4x432x4x4
D

x11xx1xx12
2131

题型九：题型九：用克拉默法则求解多元线性方程组5x16x21x5x6x0123x25x36x40x35x41问λ为何值时，齐次线性方程组（1λ）x12x24x302x13λ）x2x30xxλ）x0312（1有非零解？题型十题型十：利用行列式的基本性质来求行列式的值
a10四阶行列式0b4
0a2b30
0b2a30
b10的值等于（）0a4Ba1a2a3a4b1b2b3b4Da2a3b2b3a1a4b1b4
Aa1a2a3a4b1b2b3b4Ca1a2b1b2a3a4b3b4y行列式xxyAC2x3y32x3y3xxyyxyyxBD
2x3y32x3y3
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