Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 25 стр.

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cÈÏ Ëã
29
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c È Ï  Ë ã                                                      29
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                                                          →                                      →
         y                                                         x mˆº}Ë OÒ¹¯ºmËËä˯ËÏ}ºÓËmË}ˆº¯È
                                                          →
                                                                                                x          ¹ãº°}º°ˆ                      ¹È¯ÈããËã ӂ                            ¹ãº°}º°ˆÒ
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         z                                                                         O, g1, g 2  cÒ° 
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         x  g 2                                          º°ˆ¯ºÒä Óºm©Ë mË}ˆº¯© y  Ò z  ˆÈ} ˆº­©
                                                                                                →        →       →           →            →
        O                                                                               x = z + y È z Ò g 3 ­©ãÒ}ºããÒÓËȯөˆº
                                                               →                                                                                                                         →
       g1                                                      È m °Òã‚ }ºããÒÓËȯӺ°ˆÒ mË}ˆº¯È z  mË}
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                                                                                                ˆº¯‚ g 3  z = γ g 3 
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                       Ë¯ËÓË°« ÓÈÈ㺠mË}ˆº¯È y  m ˆº}‚ O Ò ¯È°°‚ÎÈ« }È} ¹¯Ò º}ÈÏȈËã °ˆmË
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                       ˆËº¯Ë䩹ºã‚Òä y = α g1 + β g 2 Ò°ã˺mȈËã Óº x = α g1 + β g 2 + γ g 3 
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               °         iº}ÈÎËä                     ËÒÓ°ˆmËÓÓº°ˆ                              ¯ÈÏãºÎËÓÒ«                        ¹º          ­ÈÏÒ°‚                 l©             ÒäËËä
                       →           →             →             →
                       x = α g1 + β g 2 + γ g 3  ¯Ë¹ºãºÎÒä ˆº °‚Ë°ˆm‚ˈ ¯‚È« ˆ¯º®}È Ò°Ëã
                                                                     →              →               →              →
                       α ′, β ′, γ ′ ˆÈ}Ò²ˆº x = α ′ g1 + β ′ g 2 + γ ′ g 3 
               
                       {©҈ȫ¹ºãËÓÓºªˆÒ¯ÈmËÓ°ˆmȹºã‚ÈËä
                       
                                                                                       →                          →                         →         →
                                                                      (α − α ′) g1 + ( β − β ′) g 2 + (γ − γ ′) g 3 = o 
                       
                       Ë m °Òã‚ °ËãÈÓÓºº ¹¯Ë¹ºãºÎËÓÒ« º ÓËËÒÓ°ˆmËÓÓº°ˆÒ ¯ÈÏãºÎËÓÒ«
                         α − α ′ + β − β ′ + γ − γ ′ > 0 
                                                                                               → → →
                       sºªˆººÏÓÈÈˈˆºmË}ˆº¯© {g1 , g 2 , g 3 } ãÒÓˮӺÏÈmÒ°Òä©Ò°ã˺mȈËã Óº
                       ÓË äº‚ˆ ­©ˆ  ­ÈÏÒ°ºä m °Òã‚ º¹¯ËËãËÓÒ«  ºã‚ËÓÓºË ¹¯ºˆÒmº¯ËÒË
                       º}ÈÏ©mÈˈËÒÓ°ˆmËÓÓº°ˆ ¯ÈÏãºÎËÓÒ«
               
               
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