Sponsored Links
This presentation is the property of its rightful owner.
1 / 93

第三章 线性方程组 PowerPoint PPT Presentation


  • 61 Views
  • Uploaded on
  • Presentation posted in: General

第三章 线性方程组. §1 消元法 §2 n 维向量空间 §3 线性相关性 §4 矩阵的秩 §5 线性方程组有解判别定理 §6 线性方程组解的结构. §1 消元法. 现在讨论一般线性方程组: (1) 其中 为 n 个未知量, s 为方程个数; 为.

Download Presentation

第三章 线性方程组

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


  • 1

  • 2 n

  • 3

  • 4

  • 5

  • 6


1

  • (1)

    ns


sn1


A


  • 9-1-6


1

2

3

1 123


  • 1

    1

    3 21


3


1

4

4


  • 1r=n


2r<n


7


7 1

  • r>n

  • r=nr<n


1

s<n

rs<nr<n





Back


2 n


2Pn

Pn

1

1

Pn=2n=3

n>3

3n


  • 4


5 (0,0,,0)0

  • 6


  • 7 kP

    k


  • 8 PnPn

Back


3

  • Pn

  • 9 P


n

n


  • 10



  • 1

    2

    3


11


(

  • 11` P


  • 11

    11`


11`

11


12


  • n



, 3-1-1

2

11`

3


4

, 4

  • 2n+1

    5


  • 5

    6

  • 6446


  • 2

1

2r>s


1



r>s

1


  • 1

    rs.

  • 2n+1n

    n+1n

  • 3 ,


13


  • 3

    23


  • 14

  • 2

Back


4

  • 15


3A

3


1

r<n

  • 1

    A


rr

1

2

1221||


  • 4

  • A=r=

    A



rr

ArA

||


  • 5

    An

  • AnAnn=1A|A|=|0|=0. n>1A


|A|=0

n

n=1|A|=0AA n-1n AA

Ann n


|A|=0n-1



n||


  • 5Cramer

  • 16 snAkk kAk


  • 6 rrr+1

  • ArAr+1Ar+15


Ar

rArrr

r


r rr

Ar

Arr+1Ar


Ar+1Ar+2r

Att r Art rAtr+1t=r

ArArArAr+1Ar


r


  • r(A)=r

Back


5

  • 1


1

1


  • 1


  • 1

    A A

    A r r


1||

  • A


  • CramerA rArr rr+1,,s1

    4


  • r=nCramer41

  • r<n4 5

  • 5cramer


1

Back


6

  • (1)


1

2

  • n=3

  • 17 1


1

11

2

  • 7 n-rrn-r

  • 1rr


1 3

  • r=n,r<n

    311


3n-r

(1,0,,0),(0,1,,0),,(0,0,,1) 4

31n-r

5

5


454r5

(1)

(6)

1 1

7

176n-r



  • 9

  • 19

  • 19 1

  • 291


  • 8 99

    10

    19 19

  • 1 1


9102 1

9||

  • 89

    9

  • 1


  • 11

    1111

  • 1A=1 =1A


  • 2 A=1 =2

  • 3 A=2 =2


t

13

  • 11

    14

    1113


15

13151114


R(I)=R(II)=3,R(III)=4.

4


R(I)=R(II)=3,

1


1

R(III)=4

4


  • Login