Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 29 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏ Ëã
33
{Ë}º¯©ÒãÒÓˮөËº¹Ë¯ÈÒÒ°ÓÒäÒ
ÈËº
0det
22
11
=
η
ξ
η
ξ

iº}ÈÎËäº°ÈºÓº°
°
0det
22
11
=
η
ξ
η
ξ
 ºÈ ÒäËËä º
2
2
1
1
η
ξ
η
ξ
=
¹¯Ò
0;0
21
≠≠
ηη
 º Ë°
°ººmË°mÒË }ºº¯ÒÓÈ© mË}º¯ºm
[
→
Ò
\
→
¹¯º¹º¯ÒºÓÈãÓ© º Ò
º}ÈÏ©mÈËãÒÓË®ÓÏÈmÒ°Ò亰ªÒ²mË}º¯ºm
vãÈ®
0
21
=
ηη
¹¯ËãÈÈË°«¯È°°äº¯Ë°È亰º«ËãÓº
˺¯ËäÈº}ÈÏÈÓÈ

˺¯ËäÈ

iã«ººº©¯ÒmË}º¯È
3
2
1
ξ
ξ
ξ
=
→
x

3
2
1
η
η
η
=
→
y
Ò
3
2
1
κ
κ
κ
=
→
z
m¹¯º°¯ÈÓ
°mË©ãÒãÒÓˮӺÏÈmÒ°Òä©Ó˺²ºÒäºÒº°ÈºÓºº©Ò²}º
º¯ÒÓÈ©mÓË}ºº¯ºäÈÏÒ°ËºmãËmº¯«ãÒ°ãºmÒ
0det
333
222
111
=
κη
ξ
κη
ξ
κη
ξ

iº}ÈÏÈËã°mº
¯ÒmºÒ°«m¯ÈÏËãËÙfun¡jttvnwévqoknlntqnknrzvévkµ°ä¹
vãË°mÒË

cÈmËÓ°mÈ
0det
22
11
=
η
ξ
η
ξ
Ò
0det
333
222
111
=
κη
ξ
κη
ξ
κη
ξ
°ººmË°mËÓÓº«mã«
°«Ó˺²ºÒä©äÒÒº°ÈºÓ©äÒ°ãºmÒ«äÒ}ºããÒÓËȯӺ°Ò¹È
¯©mË}º¯ºmÓÈ¹ãº°}º°ÒÒ}ºä¹ãÈÓȯӺ°Ò¯º®}ÒmË}º¯ºmm¹¯º
°¯ÈÓ°mË
iË}ȯºmÈ°Ò°ËäÈ}ºº¯ÒÓÈ
c È Ï  Ë ã                                                      33
{Ë}ˆº¯©ÒãÒÓˮө˺¹Ë¯ÈÒÒ°ÓÒäÒ



                                                        ξ1 η1
                        Èˈˆº det                         = 0 
                                                        ξ 2 η2
                  
               
               iº}ÈÎË亰ˆÈˆºÓº°ˆ 
               
                                                  ξ1 η1                           ξ   ξ
                        ‚°ˆ  det                       = 0  ˆºÈ ÒäËËä ˆº 1 = 2  ¹¯Ò η1 ≠ 0 ; η 2 ≠ 0  ˆº Ë°ˆ 
                                                  ξ 2 η2                          η1 η 2
                                                                                                                            →             →
                        °ººˆmˈ°ˆm‚ ÒË }ºº¯ÒÓȈ© mË}ˆº¯ºm [  Ò \  ¹¯º¹º¯ÒºÓÈã Ó© ˆº Ò
                        º}ÈÏ©mÈˈãÒÓˮӂ ÏÈmÒ°Ò亰ˆ ªˆÒ²mË}ˆº¯ºm
                        
                        vã‚È® η1η 2 = 0 ¹¯ËãÈÈˈ°«¯È°°äºˆ¯Ëˆ °È亰ˆº«ˆËã Óº
        
        ‘˺¯ËäȺ}ÈÏÈÓÈ
                  
                  
                  
                                                                  ξ1         η1          κ1
                                                                        →            →                  →
    ‘˺¯ËäÈ                       i㫈ººˆº­©ˆ¯ÒmË}ˆº¯È x = ξ 2  y = η 2 Ò z = κ 2 m¹¯º°ˆ¯ÈÓ
    
                                                                   ξ3         η3          κ3
                                   °ˆmË­©ãÒãÒÓˮӺÏÈmÒ°Òä©Ó˺­²ºÒäºÒº°ˆÈˆºÓºˆº­©Ò²}º
                                   º¯ÒÓȈ©mÓË}ºˆº¯ºä­ÈÏÒ°Ë‚ºmãˈmº¯«ãÒ‚°ãºmÒ 
                                   
                                                                                                      ξ1 η1 κ 1
                                                                                                  det ξ 2 η 2 κ 2 = 0 
                                                                                                      ξ 3 η3 κ 3
                  
                  
     iº}ÈÏȈËã°ˆmº
      
         ¯Òmº҈°«m¯ÈÏËãËÙfun¡jttvnwévqoknlntqnknrzvévkµ °ä¹ 
          
          
          
    
                                                                     ξ1 η1 κ 1
    
                                                  ξ1 η1
    vãË°ˆmÒË                     cÈmËÓ°ˆmÈ det        = 0 Ò det ξ 2 η 2 κ 2 = 0 °ººˆmˈ°ˆmËÓÓº«mã«
                                           ξ 2 η2
                                                                     ξ 3 η3 κ 3
                                     ˆ°«Ó˺­²ºÒä©äÒÒº°ˆÈˆºÓ©äÒ‚°ãºmÒ«äÒ}ºããÒÓËȯӺ°ˆÒ¹È
                                   ¯©mË}ˆº¯ºmÓȹ㺰}º°ˆÒÒ}ºä¹ãÈÓȯӺ°ˆÒˆ¯º®}ÒmË}ˆº¯ºmm¹¯º
                                   °ˆ¯ÈÓ°ˆmË
                  
                  
                  
iË}ȯˆºmÈ°Ò°ˆËäÈ}ºº¯ÒÓȈ

Страницы