math 01

1. K¬vkcwiwPwZ t
‡kªwb t GKv`k †kÖwb
welq t MwYZ cÖ_g cÎ
বিষয় ক োডঃ ২৬৫
বিক্ষ পবিবিবি
ক োঃ নোবিি উবিন
িহ োিী অধ্যোপ ,গবিি বিভোগ
যো বিয়োন লেজ,ঢো ো

2. g¨vwUª· I
wbY©vq
K
g¨vwUª‡·iBwZnvm
t
A‡bK¸‡jv MvwYwZK Z_¨ I DcvˇK ms‡ÿ‡c ,mn‡R I my›`ifv‡e Dc¯’vc‡bi wbwg‡Ë g¨vwUª‡·i
Avwe¯‹vi |AvaywbK MwY‡Z g¨vwUª‡·i e¨envi Acimxg| AvaywbK weÁvb , Kw¤úDUvi ,cÖ‡KŠkj
we`¨vi mKj kvLv GgbwK cwimsL¨v‡bi wewfbœ mgm¨v g¨vwUª‡·i mvnv‡h¨ ¯^í mg‡q Ges mn‡RB
mgvavb Kiv n‡”Q|1850 mv‡j me©cÖ_g Bswjk MwYZwe` †Rgm †hv‡md wmj‡f÷vi g¨vwUª‡·i cÖ_g
aviYv cÖ`vb K‡ib|1857 mv‡j MwYZwe` †Rgm †hv‡md wmj‡f÷v‡ii mnKgx© Av_v©i K¨vwj Zvi
cwÎKvq cÖ_g we‡kølYg~jKfv‡e g¨vwUª·‡K cÖKvk K‡ib|G Kvi‡Y Av_v©i K¨vwj‡K g¨vwUª‡·i RbK
ejv nq|MwY‡Z GKNvZ mgxKiY †Rv‡Ui mgvavb Kivi cÖqv‡m g¨vwUª‡·i Avwe©fve n‡jI weL¨vZ
c`v©_we` nvB‡RbevM© 1925 wL÷v‡ã †Kvqv›Uvg ejwe`¨vq g¨vwUª‡·i e¨vcK e¨envi ïiƒ nq|
ArthurCayley

3. wkLbdj mg~n-
 g¨vwUª· I g¨vwUª‡·i cÖKvi‡f` m¤ú©‡KRvb‡Z
cvi‡e|
 g¨vwUª‡·i mgZv, †hvM ,we‡qvM c×wZ m¤ú‡©K
Rvb‡Z cvi‡e|
 g¨vwUª‡·i‡hvM I we‡qvM Ki‡Zcvi‡e|
 g¨vwUª‡·i†¯‹jvi ¸wYZK m¤ú©‡KRvb‡Z cvi‡e|

4. g¨vwUª·t
hw` msL¨K msL¨v ev ivwk‡K msL¨K mvwi Ges msL¨K Kjv‡g mvwR‡q cÖ_g e›abx ev Z…Zxq
e›abx Øviv Ave× Ki‡j ‡h MvwYwZKiƒc cvIqv hvq Zv‡K g¨vwUª· e‡j| †h g¨vwUª‡·i mvwi msL¨v Ges
Kjvg msL¨v Zv wb¤œiƒc
ms‡ÿ‡c ejv hvq †h g¨vwUª· n‡jv msL¨v ev ivwki AvqZvKvi ev eM©vKvi web¨vm ev mw¾Z
MvwYwZKiƒc hv e›abx Øviv Ave×| MvwYwZK GB web¨vm ïaygvÎ Z_¨ msiÿ‡YB mxgwe× bq eis
wewfbœ MvwYwZK mgm¨v mgvav‡bI ¸iƒZ¡c~Y© f‚wgKv cvjb K‡i|‡hgb mgxKiY †Rv‡Ui mgvavb
wbY©q Kiv hvq|
mn m n
[ ]
11 12 1 1( 1) 1
21 22 2 2( 1) 2
1 2 ( 1)
1 2 ( 1)
ij
m n
A a
a a a a a
j n n
a a a a a
j n n
a a a a a
i i ij i n in
a a a a a
m m mj m n mn 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
  
 
  

  

       
       
  

       
       
  

m n

5. g¨vwUª· cÖKvkK wPý t
1. cÖ_g e›abx ( )
2. Z…Zxqe›abx [ ]
3. `yBwUDj¤^ †Rvov †iLv || ||
g¨vwUª· MVbKvix cÖ‡Z¨KwU msL¨v‡K g¨vwUª‡·i fzw³(Entry) e‡j wKš‘ G fzw³¸‡j‡K Dcv`vb ejv hv‡e bv
KviY Dcv`vb K_vwU ïaygvÎ †m‡Ui m`m¨¸‡jvi Rb¨ cÖ‡hvR¨| g¨vwUª‡·i †Kvb gvb †bB | g¨vwUª‡·i fzw³¸‡jv‡K
Bs‡iRx †QvU nv‡Zi Aÿi¸‡jv Øviv g¨vwUª·‡K Bs‡iRx eo nv‡Zi Aÿi¸‡jvØviv cÖKvk Kiv nq|
g¨vwUª· †jLvi mgq mPivPi `yBwU c`vsK(Subscript) e¨envi Kiv nq|cÖ_g c`vsK Øviv mvwi Ges wØZxq
c`vsK Øviv Kjvg wb‡`©k Kiv nq|
ms‡ÿ‡ccÖKvwkZA=[aij] g¨vwUª· Gi aij Øviv eySv‡bv nq g¨vwUª‡·i Zg mvwi I Zg Kjv‡gi fzw³|
i j
g¨vwUª‡·i hv hv _v‡K t
o fzw³ t g¨vwUª· MVbKvix cÖwZwU msL¨v‡K fzw³ e‡j|
‡Kvb g¨vwUª‡·i †gvU fzw³ msL¨v = g¨vwUª‡·i mvwi msL¨v  g¨vwUª‡·i Kjvg msL¨v
o mvwi t Avbyf‚wgK †iLv eivei Aew¯’Z msL¨v¸wj‡K ev fzw³¸‡jv‡K GK‡Îmvwi e‡j|
o Kjvg t Dj¤^ eivei Aew¯’ZmsL¨v¸wj‡K ev fzw³¸‡jv‡K GK‡Î GKwUKjvg e‡j|
o gvÎv / AvKvi /µg / chv©q t
†Kvb g¨vwUª‡·i mvwii msL¨v Ges Kjv‡gi msL¨v n‡j †K g¨vwUª‡·i µg ejv nq Ges
cov nq |
m n m n
m byn

6. g¨vwUª‡·icÖKvi‡f`

9. ‡`Iqv Av‡Q
mgm¨vt
1 0 3
6 6 4 3 2
6 5 4
A
 
    
  
6 0 18
6 25 18 12
36 30 24
A
 
   
  

10. mgm¨vt
mgvavbt

11. evwoi KvR t
1.
2.

12. ধ্নযিোদ