Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 13 стр.

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cÈÏ Ëã
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c È Ï  Ë ã                                                      17
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    vãË°ˆmÒË                  ¯Ò ˆ¯ÈÓ°¹ºÓÒ¯ºmÈÓÒÒ }mȯȈө² äȈ¯Ò mˆº¯ºº ÒãÒ ˆ¯Ëˆ ˺ ¹º
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         {ˆË¯äÒÓȲº¹¯ËËã҈ËãË®äȈ¯Òmˆº¯ºº¹º¯«}Ⱥ°ˆÈˆºÓº‚º­ÓºÁº¯ä‚
ãÒ¯‚ˈ°« ‚°ãºmÒË ºÓºÏÓÈÓº® ¯ÈÏ¯Ë Ò亰ˆÒ °Ò°ˆËä© m‚² ãÒÓˮө² ‚¯ÈmÓËÓÒ® °
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                                                               α11ξ1 + α12 ξ2 = β1
 ‘˺¯ËäÈ      iã« ˆºº ˆº­© °Ò°ˆËäÈ ãÒÓˮө² ‚¯ÈmÓËÓÒ®                        ÒäËãÈ
                                                        α 21ξ1 + α 22 ξ2 = β2
               ËÒÓ°ˆmËÓӺ˯ËËÓÒËÓ˺­²ºÒäºÒº°ˆÈˆºÓºˆº­©
                                                                                                             α11 α12
                                                                                                    det                ≠ 0 
                                                                                                             α 21 α 22
           
     iº}ÈÏȈËã°ˆmº
      
      
         iº}ÈÎËäÓ˺­²ºÒ亰ˆ 
         
         ‚°ˆ  ÈÓÓÈ« °Ò°ˆËäÈ ãÒÓˮө² ‚¯ÈmÓËÓÒ® ÒäËˈ ËÒÓ°ˆmËÓÓºË ¯Ë ËÓÒË 
         ‚¹º¯«ºËÓӂ  ¹È¯‚ Ò°Ëã {ξ1 , ξ2 }  ˆºÈ ºãÎÓ© ­©ˆ  °¹¯ÈmËãÒm©äÒ °ãË‚ 
         ÒËÒÏËË‚¯ÈmÓËÓÒ®°ººˆÓº ËÓÒ«
         
             ξ1 (α11α 22 − α12α 21 ) = ( β1α 22 − β 2α12 ) ; ξ 2 (α11α 22 − α12α 21 ) = ( β1α 21 − β 2α11 ) 
             
                                     ÒãÒ ξ1∆ = ∆1 ; ξ 2 ∆ = ∆ 2 , Ë
                                                           
                                                            α11 α12              β α12                α   β1
                                          ∆ = det                     ; ∆1 = det 1        ; ∆ 2 = det 11      .
                                                            α 21 α 22            β 2 α 22            α 21 β 2
               
                                                                                               ∆ = 0                                                                             ∆ = 0
               cÈmËÓ°ˆmÈ ξ1 ∆ = ∆ 1                            ; ξ2 ∆ = ∆ 2  ÓË m˯ө ¹¯Ò                                                           ÒãÒ ¹¯Ò                                     Ò
                                                                                               ∆1 ≠ 0                                                                            ∆ 2 ≠ 0
               ‚ºmãˈmº¯« ˆ°« ­Ë°Ò°ãËÓÓ©ä äÓºÎË°ˆmºä ¹È¯ Ò°Ëã (ξ1 , ξ2 )  ¹¯Ò
                ∆ = ∆ 1 = ∆ 2 = 0  ºªˆºä‚ ÒÏ ‚°ãºmÒ« °‚Ë°ˆmºmÈÓÒ« Ò ËÒÓ°ˆmËÓÓº°ˆÒ ¯Ë ËÓÒ«
               °ãË‚ˈˆº ∆ ≠ 0 
               
               
               iº}ÈÎË亰ˆÈˆºÓº°ˆ 

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