Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 14 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

18
Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒË°}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ
äÓºmkp
p°ãÒ
∆≠
0
ºÈÓÓÈ«°Ò°ËäÈãÒÓˮө²¯ÈmÓËÓÒ®ÒäËË¯ËËÓÒË
{, }
ξ
ξ
12
º
ÓºÏÓÈÓºº¹¯ËËã«ËäºËÏÓÈËÓÒ«äÒ
2122211211
,,,,,
ββαααα
¹ºÁº¯äãÈä
∆
∆
=
1
1
ξ
Ò
∆
∆
=
2
2
ξ

˺¯ËäÈº}ÈÏÈÓÈ

sȹ¯ÈmãËÓÓ©Ëº¯ËÏ}Ò
|¹¯ËËãËÓÒË

|¯ËϺ}¹¯«äº®}ºÓÈäÒ}ºº¯ºº°ãÎÈãËÎÈÒËÓÈÓË®º}Ò
A
Ò
B
 ÓÈÏ©mÈË°« tjwéjksnttu vzénorvu Ë°ãÒ }ÈÏÈÓº }È}È« ÒÏ ªÒ²
m²ºË}«mã«Ë°«tj·jsvuÒ}È}È«rvt|vuº¯ËÏ}È
sȹ¯ÈmãËÓÓ©®º¯ËϺ}ËäÒϺ¯ÈÎÈ°ÒämºãÒË°}Ò
AB
¹ºãÈÈ«ºº}È
A
«mã«Ë°« ÓÈÈãºä º¯ËÏ}È È º}È
B
˺ }ºÓºä jÓºÈ Óȹ¯ÈmãËÓÓ©® º¯ËϺ}
ººÏÓÈÈË°«¹¯º°º}È}
D
iãÒÓÈº¯ËÏ}ÈººÏÓÈÈË°«}È}
AB
ÒãÒ
D
°ººmË°
mËÓÓº sȹ¯ÈmãËÓÓ©®º¯ËϺ}}ºº¯ººÓÈÈãºÒ}ºÓË°ºm¹ÈÈÓÈÏ©mÈË°«tysn
kuÓȹ¯ÈmãËÓÓ©äº¯ËÏ}ºä
iË®°mÒ«°Óȹ¯ÈmãËÓÓ©äÒº¯ËÏ}ÈäÒ
|¹¯ËËãËÓÒË

imÈ ÓËÓãËm©² Óȹ¯ÈmãËÓÓ©² º¯ËÏ}È
AB
Ò
CD
°ÒÈ°« éjktuq
Ë°ãÒºÓÒ
 ãËÎÈÓÈ¹È¯ÈããËãÓ©²¹¯«ä©²
 Óȹ¯ÈmãËÓ©mºÓ°º¯ºÓ
ÒäË¯ÈmÓ©ËãÒÓ©Ë
AB CD=

{°ËÓãËm©Ëº¯ËÏ}Ò°ÒÈ°«¯ÈmÓ©äÒ¯¯
~ÈäËÒä º m °Òã º¹¯ËËãËÓÒ«  ¹È¯ÈããËãÓ©® ¹Ë¯ËÓº° Óȹ¯ÈmãËÓÓ©²
º¯ËÏ}ºmÒ²ÓËäËÓ«Ë
°ÈÓ©mÈÓȹ¯ÈmãËÓÓ©²º¯ËÏ}È
a
Ò
b


 {¯Èä}ȲÈÓÓºº}¯°È¹¯Ë¹ºãÈÈË°«ÏÓÈ}ºä°mºÒÈËã«°º°ÓºmÓ©äÒ¹ºÓ«Ò«äÒÈ}
°ÒºäÈäÒÒ˺¯ËäÈäÒªãËäËÓȯӺ®˺äË¯ÒÒÒ¹ººäºÓÒÏË°ÓË¯È°°äÈ¯ÒmÈ°«
18 Ë }  Ò Ò   } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈ÒË°}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



         
         p°ãÒ ∆ ≠ 0 ˆºÈÓÓÈ«°Ò°ˆËäÈãÒÓˮө²‚¯ÈmÓËÓÒ®ÒäËˈ¯Ë ËÓÒË {ξ1 , ξ2 } º
                                                                                                                                         ∆1
              ÓºÏÓÈÓºº¹¯ËËã«ËäºËÏÓÈËÓÒ«äÒ α11 ,α12 ,α 21 ,α 22 , β1 , β 2 ¹ºÁº¯ä‚ãÈä ξ1 =                                          Ò
                                                                                                                                         ∆
                     ∆2
              ξ2 =      
                     ∆
         
         ‘˺¯ËäȺ}ÈÏÈÓÈ
               
               
               
               
sȹ¯ÈmãËÓө˺ˆ¯ËÏ}Ò
               
               
               
    |¹¯ËËãËÓÒË         |ˆ¯ËϺ} ¹¯«äº® }ºÓÈäÒ }ºˆº¯ºº °ã‚ÎȈ ãËÎȝÒË ÓÈ ÓË® ˆº}Ò A Ò
    
                         B ÓÈÏ©mÈˈ°« tjwéjksntt€u vzénorvu Ë°ãÒ ‚}ÈÏÈÓº }È}È« ÒÏ ªˆÒ²
                         m‚²ˆºË}«mã«Ëˆ°«tj·jsvuÒ}È}È«rvt|vuºˆ¯ËÏ}È
               
               
        sȹ¯ÈmãËÓÓ©®ºˆ¯ËϺ}­‚ËäÒϺ­¯ÈÎȈ °ÒämºãÒË°}Ò AB ¹ºãÈÈ«ˆºˆº}È
A «mã«Ëˆ°« ÓÈÈãºä ºˆ¯ËÏ}È È ˆº}È B  ˺ }ºÓºä jÓºÈ Óȹ¯ÈmãËÓÓ©® ºˆ¯ËϺ}
º­ºÏÓÈÈˈ°«¹¯º°ˆº}È} D iãÒÓȺˆ¯ËÏ}Ⱥ­ºÏÓÈÈˈ°«}È} AB ÒãÒ D °ººˆmˈ°ˆ
mËÓÓº sȹ¯ÈmãËÓÓ©®ºˆ¯ËϺ}‚}ºˆº¯ººÓÈÈãºÒ}ºÓË°ºm¹ÈÈ ˆÓÈÏ©mÈˈ°«tysn
k€uÓȹ¯ÈmãËÓө予¯ËÏ}ºä
       
       
       
iË®°ˆmÒ«°Óȹ¯ÈmãËÓÓ©äÒºˆ¯ËÏ}ÈäÒ
               
               
    |¹¯ËËãËÓÒË         imÈ ÓËӂãËm©² Óȹ¯ÈmãËÓÓ©² ºˆ¯ËÏ}È AB  Ò CD  °ÒˆÈ ˆ°« éjkt€uq
                  Ë°ãÒºÓÒ
                                  ãËÎȈÓȹȯÈããËã Ó©²¹¯«ä©²
                                  Óȹ¯ÈmãËÓ©mºӂ°ˆº¯ºÓ‚
                                 ÒäË ˆ¯ÈmÓ©ËãÒÓ©ˆË AB = CD  
                         
                         {°ËӂãËm©Ëºˆ¯ËÏ}Ò°ÒˆÈ ˆ°«¯ÈmÓ©äÒ¯‚¯‚‚
       
       ~ÈäˈÒä ˆº m °Òã‚ º¹¯ËËãËÓÒ«  ¹È¯ÈããËã Ó©® ¹Ë¯ËÓº° Óȹ¯ÈmãËÓÓ©²
ºˆ¯ËÏ}ºmÒ²ÓËäËӫˈ
       
           ‚°ˆ ÈÓ©mÈÓȹ¯ÈmãËÓÓ©²ºˆ¯ËÏ}È a Ò b 

          {¯Èä}ȲÈÓÓºº}‚¯°È¹¯Ë¹ºãÈÈˈ°«ÏÓÈ}ºä°ˆmº҈ȈËã«°º°ÓºmÓ©äÒ¹ºÓ«ˆÒ«äÒÈ}
             °ÒºäÈäÒ҈˺¯ËäÈäÒªãËäËӈȯӺ®˺äˈ¯ÒÒÒ¹ºˆºä‚ºÓÒÏË° Ó˯Ȱ°äȈ¯ÒmÈ ˆ°«

Страницы