Invers Matriks PDF

October 6, 2022 | Author: Anonymous | Category: N/A
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Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

Hmtmtme \nrcubgmame

 MBDMIMY BGEGNY KME @M[YGCX Nekmryfef

\FJYM@ X[^KG GEOFY@M[GCM OMC^B[MX [NCEGC KME GB@^ CF@\^[NY (O[GC) ^EG_NYXG[MX GEKYM\YMX[M (^EGEKYM) \JYG 9.  Xgomt-sgomt Gevnrs @mtrgcs

 M. \nejnrtgme Gevnrs @mtrgcs @mtrgcs Kum iuma `mtrgcs pnrsnjg frkf exe, `mtrgcs M kme `mtrgcs I. @mtrgcs I kgcmtmcme gevnrs `mtrgcs M dgcm inrbmcu pnrcmbgme metmrm `mtrgcs M kme `mtrgcs I sm`m knejme pnrcmbgmme `mtrgcs I kme `mtrgcs M sm`m knejme `mtrgcs gknetgtms G. Kgtubgs4 M.I 0 I.M 0 G Gevnrs `mtrgcs M kgtubgs M -=. Xnagejjm4 M.M -= 0 M -= . M 0 G

@mtrgcs ymej `n`gbgcg gevnrs kgsniut `mtrgcs gevnrtgibn mtmu `mtrgcs efesgejubmr. Xnkmejcme `mtrgcs ymej tgkmc `n`gbgcg gevnrs kgsniut `mtrgcs sgejubmr. Dgcm M mkmbma `mtrgcs sgejubmr `mcm kntnr`geme `mtrgcs M sm`m knejme efb. Kgtubgs4 knt M 0 |M| 0 < Yu`us u`u` gevnrs `mtrgcs mkmbma4  M=  

=  M

. mkd  M  

--------------------- \nrsm`mme >.=

Cntnrmejme4  M -=  |M| mkd M

4 Gevnrs `mtrgcs M 4 Kntnr`geme `mtrgcs M 4 Mkdfget `mtrgcs M

Ambm`me 9

 

 

Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

I. Gevnrs @mtrgcs Frkf 9x9 Xumtu `mtrgcs M frkf 9x9  m

i 

 M   



  k  

 h

Kntnr`geme `mtrgcs M 0 knt M 0 |M| mkmbma4 |M| 0 (mk)  ‘ (ih)  Mkdfget `mtrgcs `mtrgcs M mkmbma4   k    h

mkdM   

 i    m  

Xnagejjm gevnrs `mtrgcs M frkf 9x9 mkmbma4  M=  

 M= 

=  M

. mkd  M  

  k  =   . h mk   ih  

 i      --------------------- \nrsm`mme >.9 m  

Hfetfa >-=  =

 M   

 8

 9      ; 

Kgcntmaug `mtrgcs `mtrgcs M frkf 9x9. Hmrgbma gevnrs ` `mtrgcs mtrgcs M

Dmwmi  M= 

=



 M

  k  =   . h mk   ih  

  ;  =.(;)  ( 9).8. .   8 =

 M = 

  ;  ;  ?.   8

 M = 

=   ; . 9.    8

 M

=

 i     m  

=

   9  8    9

. 

 ( 9)   =    

9) 



  =  

9) 



  =  

=)  = 



9 

Ambm`me 8

 

 

Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

H. Gevnrs @mtrgcs Frkf 8x8 knejme Mkdfget @mtrgcs Xumtu `mtrgcs M frkf 8x8

 m==   M   m9=

m=9

m=8  

m99

m98   

   m8=

m89

m88   

 





\nenetume kntnr`geme `mtrgcs M mtmu knt M 0 |M| kmpmt kgtnetucme knejme `ntfkn Xmrrus mtmu `ntfkn Ncspmesg cfomctfr tnramkmp imrgs mtmu tnramkmp cfbf`.

 



Cfomctfr tgmp nbn`ne `mtrgcs mkmbma4 Hgd 0 (-=)(g+d) . @gd  Knejme kn`gcgme cfomctfr tgmp nbn`ne `mtrgcs frkf 8x8 mkmbma4

 

(=)= = . @      ==  





H =9

 ( =)= 9 . @   =9   @ =9  . 

H =8



(=)

H 9=



( =) 9 = . @   9= 

H 99



( =) 9 9 . @    99 



H 98



(=) 9 8 . @   98 

  @ 98 

H 8=



(=) 8 = . @      8=

H 89



(=) 8 9 . @  89

H 88



(=) 8 8 . @     ==

= 8

 

 

 

 

 

 

 



. @    =8 













 @ ==

.

H ==





 @ =8



m 98 m88

m 9=

m 99

m8=

m89

m=9

m=8

m89

m88

m==

m=8

m8=

m88

m==

m=9

m8=

m89

m=9

m=8

m 99

m 98

m==

m=8

m 9=

m 98

m==

m=9

m 9=

m 99

.



.

 @ 88

m 9= m8=

.



  @ 89 



m88  



.

 @ 8=

m89

.





m98



  @ 9= 

 @ 99

m99

.

.



 

 

 

 

 

 

 

 

Ambm`me ;

 

 

Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

@mtrgcs Cfomctfr frkf 8x8 kmpmt kgtubs4

   @ ==  H      @ 9=     @ 8=

  @ =9   @ 99   @ 89

  @ =8      @ 98       @ 88 

   Mkdfget @mtrgcs @mtrgcs mkmbma [ [rmespfsn rmespfsn kmr kmrgg Cfomctfr



     @ == mkdM  H      @ =9     @ =8  



       [  mkdM  H          

  @ 9=   @ 99   @ 98

m99

m98

m89 m9=

m88 m98

m8= m9=

m88 m99

m8=

m89

  

  @ 8=     @ 89       @ 88  m=9

m=8

m89 m==

m88 m=8

m8= m==

m88 m=9

m8=

m89

  

m=9

m=8  

m99 m==

m98  m=8 

m9= m==

m98  m=9 

m9=

   

 m99  

Gevnrs `mtrgcs frkf 8x8 mkmbma4  M=  

 M=

=  M

. mkd  M

    =   .   M      

 

m99

m98

m89 m9=

m88 m98

m8= m9=

m88 m99

m8=

m89

  

m=9

m=8

m89 m==

m88 m=8

m8= m==

m88 m=9

m8=

m89

  

m=9

m=8  

m99 m==

m98  m=8 

m9= m==

m98  m=9 

m9=

   

 m99  

Hfetfa >-9

 =   \    9   =

9 8 9

= 

Kgcntmaug `mtrgcs \ frkf 8x8 pmkm jm`imr kg sm`pgej.  Hmrgbma gevnrs `mtrgcs \ ;    8 

Dmwmi4 @nenetucme kntnr`geme `mtrgcs \, ifbna `nejjuemcm `nejjuemcme e `ntfkn Xmrrus mtmu `ntfkn ncspmesg cfomctfr.

Ambm`me >

 

 

Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

@gsmbeym `nenetucme kntnr`geme `mtrgcs \ `nejjuemcme `ntfkn ncspmesg cfomctfr tnramkmp imrgs cn-9

 =   \    9   =

Gejmt4 (-=) pmejcmt jmedgb 0 -= (-=) pmejcmt jnemp 0 =

= 

9

 ;    8 

8 9

 \   ()(9).

9

=

9

8

   (8)

=

=

=

8

 ( )(;)

=

9

=

9

 

 \   ()(9).(?  9)  (8).(   8  =)  ()(;).(9  9)    \   1  ?   <   9  

Xnbmeduteym `nenetucme `mtrgcs cfomctfr

   @ ==  H      @ 9=     @ 8=      H          

8

;

9 9

8 =

9 9

8 =

8

;

  =  H    ;    >

  @ =9   @ 99   @ 89   

  @ =8      @ 98       @ 88 

9

;

= =

8 =

= =

8 =

9

;

9

=  

9

<      = 

  

9

8  

= =

9 9 

= =

9  9

9

 8  

   



9

 Mkd \ mkmbma trmespfsn km kmrg rg `mtrgcs cf cfomctfr omctfr H

  =  mkd \   H [     9    =

; 9 <

>  

  9     = 

Gevnrs `mtrgcs \ mkmbma4  \ =  

 \ =

=  \ 

. mkd \ 

  =   9 9   = = 

 

; 9 <

     9   =     =    >  

9

= <

Ambm`me ?

 9,>   =     

 

 

Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

K. Gevnrs @mtrgcs 8x8 knejme [rmesofr`msg Imrgs Nbn`netnr  @nenetucme gevnrs `mtrgcs knejme hmrm trmesofr`msg imrgs nbn`netnr kgcnemb dujm knejme `ntfkn fpnrmsg imrgs nbn`netnr (FIN). Hmrm ymej kgbmcucme mkmbma4 =.  @n`iumt `mtrgcs `nedmkg `mtrgcs muj`netnk, ymgtu `mtrgcs ymej kgpnrinsmr. Kgpnrinsmr ymej kg`mcsuk mkmbma `nem`imacme `mtrgcs gknetgtms kgsninbma cmeme knejme frkf ymej sm`m knejme `mtrgcs ymej mcme kghmrg gknetgtmseym. @mtrgcs M `nedmkg inetuc `mtrgcs muj`netnk SM|GP

 m==   M   m9=   m8=

m=9

m=8  

m99

m98 

m89



 m88  

 

Kgiumt `nedmkg `mtrgcs muj`netnk (Muj`netnk @mtrgx)

 m ==   m9=   m8=

m

m

=9

=8

|

=

<

    =    

@mcm gevnrs \ mkmbma4 =

 \ 

    =   

9

= <

 9,>  =      

N. Xgomt-sgomt Gevnrs @mtrgcs  Inrgcut tnrkmpmt ininrmpm sgomt ‘sgomt kmrg `mtrgcs pnrsnjg ymej `n`pueymg gevnrs. =.  (M.I)-= 0 I-=. M -=  9.  (I.M)-=0 M -= . I-=  8.  (M -=)[0 (M [)-= 

Ambm`me 1

°I9+I8

-9I9+I=

-²I=+I9

Xnbnsmg

 

 

Nekmryfef ‘ Imi _  ‘ Gevnrs @mtrgcs

[^JMX  >  ‘ 

Cnrdmcme kg cnrtms knejme tubgsme tmejme. (ifbna A_X mtmu Ofbgf inrjmrgs). Dmejme bupm hmetu`cme em`m kme E\@  VVVVVVVVVVVVVVVVVVVVVVVVVVVVV  VVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVVVVVVVVVVVVVVVVVVVV VVVVVV

Kgcntmaug sumtu `mtrgcs M

  =   M    9  =  

=

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