Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 121 стр.

UptoLike

Составители: 

Рубрика: 

cÈÏËã

¯Ëº¯ÈϺmÈÓÒ«¹ãº°}º°Ò
˺¯ËäÈ

iã«ãº®ãÒÓÒÒ mº¯ºº ¹º¯«}È}ÈÏÈÓÓº®mÁº¯äãÒ¯ºm}Ë˺
¯Ëä©ÒÓË«mã«Ë®°«¹°©ääÓºÎ˰mºä

¹¯ÒÈÁÁÒÓÓºä¹¯Ëº¯ÈϺmÈÓÒÒËËÒ¹ÓËäºÎËÒÏäËÓÒ °«
ÓÈ®Ë°« ÈÁÁÒÓÓºË ¹¯Ëº¯ÈϺmÈÓÒË ¹Ë¯Ëmº«ËË ËË m ã
¯ãÒÓÒmº¯ºº¹º¯«}ÈªººÎËÒ¹È
iº}ÈÏÈËã°mº
cȰ°äº¯Òä¹Ë¯mºËm˯ÎËÓÒË˺¯Ëä©
°{°Òã˺¯ËäÒ¹È¯ÈããË㺯Èäämä˰Ë°º°mºË®mÓ¯ËÓÓË®È
°¹Ë¯Ë²ºÒm¹È¯ÈããË㺯Èää Ò ÏÓÈÒº¯ÈÓÒËÓÓÈ«}¯ÒmÈ«¹Ë¯Ë®Ë
m º¯ÈÓÒËÓÓ |°È °ãËË º ªããÒ¹°© Ò º}Ò äº ¹Ë¯Ë²ºÒ
ºã}ºmªããÒ¹°©Òº}Òv¯º®°º¯ºÓ©º}ÈÓËäºÎË¹Ë¯Ë²ºÒm
ªããÒ¹° Ò ÓȺº¯º ¹º°}ºã} ªº ¹¯ºÒmº¯ËÒ °mº®°m mÏÈÒäÓº® ºÓº
ÏÓÈÓº°ÒÈÁÁÒÓÓºº¹¯Ëº¯ÈϺmÈÓÒ«
°v¯ËÒ ãÒÓÒ® mº¯ºº ¹º¯«}È ºã}º ҹ˯ºã© Ò ¹È¯ÈããËãÓ©Ë ¹¯«ä©Ë
ÒäË Ó˰m«ÏÈÓÓ©Ë mËmÒ º ˰ °˰mË ¹¯«äÈ« ÓË ¹Ë¯Ë°Ë}ÈÈ«
ãÒÓÒmº¯ºº¹º¯«}ÈÈ}È«ºmËmÒªº®ãÒÓÒÒ¯È°¹ºãºÎËÓ©¹º¯ÈÏÓ©Ë
°º¯ºÓ© º ¹¯«äº® iÈÓÓºË °mº®°mº ºËmÒÓº°º²¯ÈÓ«Ë°« ¹¯Ò ÈÁÁÒÓÓºä
¹¯Ëº¯ÈϺmÈÓÒÒ ȯÈããËãÓ©Ë ÎË ¹¯«ä©Ë ÓË äº ¹Ë¯Ë®Ò m mËmÒ Ò
¹Ë¯ºã©m°Òã˺¯Ëä©
°v¯ËÒÓ˹¯«ä©²ãÒÓÒ®mº¯ºº¹º¯«}Èºã}º¹È¯ÈºãÈ«mã«Ë°«Ó˺¯È
ÓÒËÓÓº® °m«ÏÓº® }¯Òmº® vã˺mÈËãÓº ¹¯Ò ÈÁÁÒÓÓºä ¹¯Ëº¯ÈϺmÈÓÒÒ
¹È¯ÈºãÈäºÎË¹Ë¯Ë®Òºã}ºm¹È¯Èºã
°p°ãÒ ãÒÓÒ« mº¯ºº ¹º¯«}È ˰º}È ¹¯«äÈ« ÒãÒ ÎË ¹È¯È ¹È¯ÈããËãÓ©²
ÒãÒ¹Ë¯Ë°Ë}ÈÒ²°«¹¯«ä©²ºÒÏm˯ÎËÓÒ«˺¯ËäÒm©Ë
}ÈËºÒ²Ò¹ÓËäºÎËÒÏäËÓÒ°«
cȰ°äº¯Òämº¯ºËm˯ÎËÓÒË˺¯Ëä©
jÏ˺¯ËäÒ°ãËËºã«}Èκ®ãÒÓÒÒmº¯ºº¹º¯«}Èäº
ÎË©¹º°¯ºËÓºÈÁÁÒÓÓºË¹¯Ëº¯ÈϺmÈÓÒË¹¯Òmº«ËË¯ÈmÓËÓÒËãÒ
ÓÒÒ}ºÓºäÒÏ°ãËÒ²Ëm«ÒmÒºm

+
=
±
=
±=
=
=
xy xy
xy y y x y
22 22
22 2 2 2
11
010200
;
;; ;.

sº ¹º°}ºã} ¯ÈmÓËÓÒ« ãº® ¹È¯© ãÒÓÒ® ¹¯ÒÓÈãËÎÈÒ² } ºÓºä Ò
ºäÎËÒ¹¹¯Òmº«°«mä«¯ÈÏãÒÓ©äÒÈÁÁÒÓÓ©äÒ¹¯Ëº¯ÈϺmÈÓÒ«äÒ
} ºÓºäÒºäÎËmÒ ÒÏ °¹Ò°}È   º m °Òã mÏÈÒäÓº®
cÈÏËã
¯Ëº­¯ÈϺmÈÓÒ«¹ãº°}º°ˆÒ



    ‘˺¯ËäÈ             iã« ã ­º® ãÒÓÒÒ mˆº¯ºº ¹º¯«}È ‚}ÈÏÈÓÓº® m Áº¯ä‚ãÒ¯ºm}Ë ˆËº
                  ¯Ëä©ÒÓË«mã« Ë®°«¹‚°ˆ©ääÓºÎ˰ˆmºä
                              
                           ¹¯ÒÈÁÁÒÓӺ乯˺­¯ÈϺmÈÓÒÒËˈҹÓËäºÎˈÒÏäËÓ҈ °«
                           
                           ÓÈ®ˈ°« ÈÁÁÒÓÓºË ¹¯Ëº­¯ÈϺmÈÓÒË ¹Ë¯Ëmº«ËË ËË m ã ­‚ 
                                ¯‚‚ ãÒÓÒ mˆº¯ºº¹º¯«}ȪˆººÎˈҹÈ
             
             
     iº}ÈÏȈËã°ˆmº
      
      

          cȰ°äºˆ¯Òä¹Ë¯mºË‚ˆm˯ÎËÓÒˈ˺¯Ëä©
          
          °{°Òよ˺¯ËäҹȯÈããË㺯Èäämä˰ˆË°º°mºË®mӂˆ¯ËÓÓË®È
               °ˆ  ¹Ë¯Ë²º҈ m ¹È¯ÈããË㺯Èää Ò ÏÓÈ҈ º¯ÈÓÒËÓÓÈ« }¯ÒmÈ« ¹Ë¯Ë®ˈ
               m º¯ÈÓÒËÓӂ  |ˆ° È °ãË‚ˈ ˆº ªããÒ¹°© Ò ˆº}Ò äº‚ˆ ¹Ë¯Ë²º҈ 
               ˆºã }º m ªããÒ¹°© Ò ˆº}Ò v ¯‚º®°ˆº¯ºÓ©ˆº}ÈÓËäºÎˈ¹Ë¯Ë²º҈ m
               ªããÒ¹° Ò ÓȺ­º¯ºˆ ¹º°}ºã }‚ ªˆº ¹¯ºˆÒmº¯Ë҈ °mº®°ˆm‚ mÏÈÒäÓº® ºÓº
               ÏÓÈÓº°ˆÒÈÁÁÒÓÓºº¹¯Ëº­¯ÈϺmÈÓÒ«
          
          °v¯ËÒ ãÒÓÒ® mˆº¯ºº ¹º¯«}È ˆºã }º ҹ˯­ºã© Ò ¹È¯ÈããËã Ó©Ë ¹¯«ä©Ë
               ÒäË ˆ Ó˰m«ÏÈÓÓ©Ë mˈmÒ ˆº ˰ˆ  °‚Ë°ˆm‚ˈ ¹¯«äÈ« ÓË ¹Ë¯Ë°Ë}È È«
               ãÒÓÒ mˆº¯ºº¹º¯«}ȈÈ}È«ˆºmˈmÒªˆº®ãÒÓÒүȰ¹ºãºÎËÓ©¹º¯ÈÏÓ©Ë
               °ˆº¯ºÓ© ºˆ ¹¯«äº® iÈÓÓºË °mº®°ˆmº ºËmÒÓº °º²¯Èӫˈ°« ¹¯Ò ÈÁÁÒÓÓºä
               ¹¯Ëº­¯ÈϺmÈÓÒÒ È¯ÈããËã Ó©Ë ÎË ¹¯«ä©Ë ÓË äº‚ˆ ¹Ë¯Ë®ˆÒ m mˈmÒ Ò
               ¹Ë¯­ºã©m°Òよ˺¯Ëä©
          
          °v¯ËÒÓ˹¯«ä©²ãÒÓÒ®mˆº¯ºº¹º¯«}Ȉºã }º¹È¯È­ºãÈ«mã«Ëˆ°«Ó˺¯È
               ÓÒËÓÓº® °m«ÏÓº® }¯Òmº® vã˺mȈËã Óº ¹¯Ò ÈÁÁÒÓÓºä ¹¯Ëº­¯ÈϺmÈÓÒÒ
               ¹È¯È­ºãÈäºÎˈ¹Ë¯Ë®ˆÒˆºã }ºm¹È¯È­ºã‚
          
          °p°ãÒ ãÒÓÒ« mˆº¯ºº ¹º¯«}È ˰ˆ  ˆº}È ¹¯«äÈ« ÒãÒ ÎË ¹È¯È ¹È¯ÈããËã Ó©²
               Òãҹ˯˰Ë}È Ò²°«¹¯«ä©²ˆºÒÏ‚ˆm˯ÎËÓÒ«ˆËº¯ËäÒm©ˆË
               }ÈˈˆºÒ²ˆÒ¹ÓËäºÎˈÒÏäËÓ҈ °«
          
          
          cȰ°äºˆ¯Òämˆº¯ºË‚ˆm˯ÎËÓÒˈ˺¯Ëä©
          
          
               jψ˺¯ËäÒ°ãË‚ˈˆºã«}Èκ®ãÒÓÒÒmˆº¯ºº¹º¯«}Èäº
               Îˈ­©ˆ ¹º°ˆ¯ºËÓºÈÁÁÒÓӺ˹¯Ëº­¯ÈϺmÈÓÒ˹¯Òmº«ËË‚¯ÈmÓËÓÒËãÒ
               ÓÒÒ}ºÓºä‚ÒϰãË‚ Ò²Ëm«ˆÒmÒºm
               
               
                                 x ′ 2 + y ′ 2 = ±1 ;         x′2 − y′2 = 1
                                                                                                                      
                                 x′2 ± y′2 = 0 ;             y′2 ± 1 = 0 ;           y ′ 2 − 2x ′ = 0 ;          y′2 = 0 .
                 
                 
                 sº ¹º°}ºã }‚ ‚¯ÈmÓËÓÒ« ã ­º® ¹È¯© ãÒÓÒ® ¹¯ÒÓÈãËÎȝҲ } ºÓºä‚ Ò
                 ˆºä‚Îˈҹ‚¹¯Òmº«ˆ°«m‚䫯ÈÏãÒÓ©äÒÈÁÁÒÓÓ©äÒ¹¯Ëº­¯ÈϺmÈÓÒ«äÒ
                 } ºÓºä‚ Ò ˆºä‚ ÎË mÒ‚ ÒÏ °¹Ò°}È    ˆº m °Òã‚ mÏÈÒäÓº®