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

n n

nn n

n

n n

n n

b x

a x

a x

a

b x

a x

a x

a

b x

a x

a x

a

2 2 1

1

2 2

2 22 1

21

1 1

2 12 1

11

, ,

, , 2

1 不全为零

(3)

) 1 (

2 2 1

1

2 2

2 22 1

21

1 1

2 12 1

11



n n

nn n

n

n n

n n

b x

a x

a x

a

b x

a x

a x

a

b x

a x

a x

a

nn n

n

n n

a a

a

a a

a

a a

a D

2 1

2 22

21

1 12

11

0

(4)

1

1 2

2 3

2

n

n

Dj D j

n

nn j

, n n

j , n n

n j

, j

,

j

1 1

1

1 1

1 1

1 1 11

1

(5)

nj n

nj n

nn n

n

j j

n n

j j

n n

2 2 1

1

2 2 2

2 2

22 1

21

1 1 1

1 2

12 1

11

, 1

, ,

, 2

1

n

A A

A j

D j jnj

(6)

,

1

1 1

1 1

1



 

 



 

 



 

n k

kj k

n n

k

kj kn j

n k

kj kj n

k

kj k

A b

x A

a x

A a

x A

a  

j 1,2, ,n

.

D

Dxjj  

1

1 2

2 3

2

n

n

, D xj的系数等于 上式中

2

2

(7)

2

1

1

1 2

2 3

2

n

n

1

(8)

## 二、重要定理

1

1 D 0,

1

(9)

2 2 1

1

2 2

22 1

21

1 2

12 1

11

n nn n

n

n n

n n

2

2

(10)

###  

2 有非零解 , 则它 的系数行列式必为零 .





0 0 0

2 2 1

1

2 2

22 1

21

1 2

12 1

11

n nn n

n

n n

n n

x a

x a

x a

x a

x a

x a

x a

x a x

a

(11)





. 0 6

7 4

, 5 2

2

, 9 6

3

, 8 5

2

4 3

2 1

4 3

2

4 2

1

4 3

2 1

x x

x x

x x

x

x x

x

x x

x x

6 7

4 1

2 1

2 0

6 0

3 1

1 5

1 2

D r12r2

2

4 r

r

12 7

7 0

2 1

2 0

6 0

3 1

13 5

7 0

(12)

12 7

7

2 1

2

13 5

7

c12c2

2

3 2c

c

2 7

7

0 1

0

3 5

3

2 7

3 3

   27,

6 7

4 0

2 1

2 5

6 0

3 9

1 5

1 8

1

D

,

81

6 7

0 1

2 1

5 0

6 0

9 1

1 5

8 2

2

D

,

108

(13)

6 0

4 1

2 5

2 0

6 9

3 1

1 8

1 2

3

  D

,

27

0 7

4 1

5 1

2 0

9 0

3 1

8 5

1 2

4

D

,

27

, 27 3

1 81

1

D

x D 4,

27

2 108

2

D x D

, 27 1

3 27

3

D

x D 1.

27

4 27

4

D x D

(14)





. 6 5 2

3

, 6 11 ,

4 4

3

, 3 2

5 3

4 3

2 1

4 3

2 1

4 2

4 3

2 1

x x

x x

x x

x x

x x

x x

x x

0,

(15)

2 3 1

6 5

1 1

1 6

11

4 0

3 4

1 2

5 3

1

D ,

3

67

2 3

6 5 1

1 1

6 11 1

4 0

4 0

1 2

3 3

2

D0,

2 6

5 1

1

1 6

11 1

1

4 4

3 0

1 3

5 3

3

D ,

2

67

6 5 3

1 1

6 11 1

1 1

4 0

3 0

3 2

5 3

4

D 67,

(16)

D , x D

3 1 67

673

1

1   

,

D

x D 0

67

2 0

2   

D , x D

2 1 672

67

3

3    1.

67

4 67

4

D x D



, 0 1

, 0 3

2

, 0 4

2 1

3 2

1

3 2

1

3 2

1

x x

x

x x

x

x x

x

(17)

1 1

1

1 3

2

4 2

1 D

1 0

1

1 1

2

4 3

1

1 3 3 4 1 2 1 3

1

3 2

1

2 3

   

0,

2

### 

3

(18)

1. 用克拉默法则解方程组的两个条件 (1) 方程个数等于未知量个数 ;

(2) 系数行列式不等于零 .

2. 克拉默法则建立了线性方程组的解和已知的系 数与常数项之间的关系 . 它主要适用于理论推导 .

(19)

(20)

## 思考题解答

Later, we will relate the φ-ﬁxed ideals with the ideals coming from a resolution of singularities in characteristic 0 (e.g. multiplier ideals, Fujino’s non-LC ideal, and the

• A conditional jump instruction branches to a label when specific register or flag conditions are met.

[r]

The existence and the uniqueness of the same ratio points for given n and k.. The properties about geometric measurement for given n

[r]

The Seed project, REEL to REAL (R2R): Learning English and Developing 21st Century Skills through Film-making in Key Stage 2, aims to explore ways to use film-making as a means