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VED1
          E\L-LOVELY-H\math18-1 IInd 21-10-11  IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12 VIIth 11-5-13


                                                                                   bdkbZ     vkO;wg % vFkZ ,oa izdkj




          18-3 vkO;wg osQ izdkj  ! 
 
    *    )                                                   uksV


                oxZ vkO;wg
          ;fn fdlh vkO;wg esa iafDr;ksa ,oa LrEHkksa dh la[;k cjkcj gS rc mls oxZ vkO;wg dgrs gSaA vFkkZr~ ;fn   ,
            gks rks vadk;r dks   Øe dk oxZ O;wg dgrs gSaA vU; O;wg tgk¡ gksa os vk;rkdkj O;wg dgykrs gSaA mnkgj.kkFkZ]
                                                     1  2   3
                                         2  3              
                                   
 ,         B =− 2  4   0 
                                                   
                                         − 1  7       7  2  5  

          mijksDr nksuksa O;wg oxZ vkO;wg gSa ftuosQ Øe    9    rFkk  ! 9 !  gSaA
                iafDr vkO;wg  ! "

          ;fn   ,  - rc vkO;wg esa osQoy ,d iafDr jgsxh] bls iafDr vkO;wg dgsaxsA mnkgj.kkFkZµ
                                   
 , .  !/
                                     , .2'   4/
                                     , .  ! 4 2;/
                LrEHk vkO;wg    # $

          ;fn   ,  - rc vkO;wg esa osQoy ,d LrEHk jgsxk vkSj iafDr;ksa dh la[;k;sa vusd] bls LrEHk vkO;wg dgsaxsA
          mnkgj.kkFkZ]
                                                               1 
                                                    2       
                                        1                  2
                                   
 ,     , B =− 1   , C =  
                                                  
                                                               4 
                                        3
                                        21        0       
                                           ×
                                                     
                                                  
                                                      31
                                                       ×
                                                               7 
                                                               41
                                                                  ×
            %  'kwU; vkO;wg  & ##	      	  	'
          ;fn fdlh vkO;wg osQ lHkh vo;o 'kwU; gksa] rks og 'kwU; vkO;wg dgykrk gSA mnkgj.kkFkZ]
                                                                     0   0  0
                                                 0     0   0             
                                   
 , .4 4/-   ,   , C =     , D =    0  0  0 
                                                 0
                                                       0  0 
                                                                      0   0  0  
          mi;qZDr lHkh 'kwU; vkO;wg gSaA 'kwU; vkO;wg dks   cM+s    >      v{kj ls fy[kk tkrk gSA   'kwU; ugha gS]
          ;g osQoy vkO;wg dk laosQr gSA
            %  rRled ;k bdkbZ vkO;wg   (     )	  	*
          ;g ,d oxZ vkO;wg gS ftlosQ lHkh fod.kZ vo;o  @    
        
 
  bdkbZ gSa vkSj vU; vo;o 'kwU;
          gSaA bls rRled ;k bdkbZ vkO;wg dgrs gSaA mnkgj.kkFkZ]
                                                                    1   0  0  0
                                                    1   0  0                  
                                        1   0                   0  1   0   0
                                   
 ,        ; B =    0  1  0 ; C =        
                                         0  1     0   0  1      0   0  1  0
                                                                   0   0  0  1     

           %   fod.kZ vkO;wg  +  ,   #

          ;fn fdlh oxZ vkO;wg osQ izeq[k fod.kZ ij fLFkr vo;oksa dks NksM+dj 'ks"k lc 'kwU; gSa] rc mls fod.kZ vkO;wg
          dgrs gSaA mnkgj.kkFkZ]
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