Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 26 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

30
Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒË°}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ
äÓºmkp
|¹¯ËËãËÓÒË

Ò°ãÈ
γ
βα
,,
}ºªÁÁÒÒËÓ©m¯ÈÏãºÎËÓÒÒ
→→→→
++=
321
gggx
γ
βα
ÓÈ
Ï©mÈ°« }vvélqtjzjuq ÒãÒ rvuwvtntzjuq mË}º¯È
x
→
m ÈÏÒ°Ë
},,{
321
→→→
ggg

iã« ÏȹҰÒ mË}º¯È
→→→→
++=
321
gggx
γ
βα
m }ºº¯ÒÓÈÓºä ¹¯Ë°ÈmãËÓÒÒ
Ò°¹ºãÏ°«Áº¯ä©
°

);;(
γ
βα
→
x

°

(;;)
αβ
γ

°

αβ
γ



°

α
β
γ

°

α
β
γ

ÒÏ}ºº¯©²mÈãÓË®Ëää©ËäÒ°¹ºãϺmÈ¹º°ãËÓ
{ºËä°ãÈËm˯ÎËÓÒËknrzvé
x
→
kijoqxn
},,{
321
→→→
ggg
qunnzrvvélqtjz
tvn wénlxzjksntqn
α
β
γ
ÏȹҰ©mÈË°«}È}
x
g
→
=
α
β
ÓºÒÓºÈË°ãÒªºÓË¹¯Òmº
Ò}Ó˺ӺÏÓÈÓº°Òºã}ºmÈÓÒ«ä©ËäÒ°¹ºãϺmÈÒ°º}¯ÈËÓÓÏȹҰmÒÈ
x
→
=
α
β
γ

sÈ}ºÓË Ë°ãÒ mË}º¯
x
→
m ÈÏÒ°Ë
{, }gg
12
→→
ÓÈ ¹ãº°}º°Ò ¹¯Ë°ÈmÒä }È}
xgg
→→→
=+
αβ
12
º˺}ºº¯ÒÓÈÓÈ«ÏȹҰÒäËËmÒ
x
g
→
=
α
β

iË®°mÒ«°mË}º¯ÈäÒm}ºº¯ÒÓÈÓºä¹¯Ë°ÈmãËÓÒÒ
º°}ºã}m }ºÓ}¯ËÓºäÈÏÒ°Ë
},,{
321
→→→
ggg
}ÈΩ®mË}º¯ÓȲºÒ°«mºmÏÈ
ÒäÓººÓºÏÓÈÓºä°ººmË°mÒÒ°¹º¯«ºËÓÓº®¯º®}º®Ò°Ëã
γ
βα
,,
°mºÒäÒ}º
30 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



                                                                                                         →       →       →         →
 |¹¯ËËãËÓÒË              Ò°ãÈ α , β , γ }ºªÁÁÒÒËӈ©m¯ÈÏãºÎËÓÒÒ x = α g1 + β g 2 + γ g 3 ÓÈ
                                                                                                                   →
                         Ï©mÈ ˆ°« }vvélqtjzjuq ÒãÒ rvuwvtntzjuq  mË}ˆº¯È x  m ­ÈÏÒ°Ë
                           → → →
                         {g1, g 2 , g 3 } 
              
              
                                                     →         →        →            →
       iã« ÏȹҰÒ mË}ˆº¯È                          x = α g1 + β g 2 + γ g 3  m }ºº¯ÒÓȈӺä ¹¯Ë°ˆÈmãËÓÒÒ
Ò°¹ºã ς ˆ°«Áº¯ä©
                                →
                          ° x ( α ; β ; γ ) ° (α ; β ; γ ) ° α              β γ 
                                                                          
                              α                                α
                               
°  β  ° β 
                               
                              γ                                γ
ÒÏ}ºˆº¯©²mÈã ÓË® Ëää©­‚ËäÒ°¹ºã ϺmȈ ¹º°ãËÓ                                                

       
                                                                             →                       → → →
              {º­Ëä°ã‚ÈË‚ˆm˯ÎËÓÒËknrzvé x kijoqxn {g1 , g 2 , g 3 } qunnzrvvélqtjz
                   α                                                                   α
                                          →
tvnwénlxzjksntqn β ÏȹҰ©mÈˈ°«}È} x                                          = β ÓºÒÓºÈË°ãÒªˆºÓ˹¯Òmº
                   γ                                                                   γ
                                                                                 g

҈}Ó˺ÓºÏÓÈÓº°ˆÒˆºã}ºmÈÓÒ«ä©­‚ËäÒ°¹ºã ϺmȈ Ò°º}¯ÈËÓӂ ÏȹҰ mÒÈ
    α
→
x = β 
    γ
              
                                                      →                          →       →
              sÈ}ºÓË Ë°ãÒ mË}ˆº¯ x  m ­ÈÏÒ°Ë {g1 , g 2 }  ÓÈ ¹ãº°}º°ˆÒ ¹¯Ë°ˆÈmÒä }È}
→         →        →                                                                         →            α
x = α g1 + β g 2 ˆºËº}ºº¯ÒÓȈÓÈ«ÏȹҰ ÒäËˈmÒ x                                           =      
                                                                                                 g        β
              
              
              
              
iË®°ˆmÒ«°mË}ˆº¯ÈäÒm}ºº¯ÒÓȈӺ乯˰ˆÈmãËÓÒÒ
              
              
              
                                                                      → → →
              º°}ºã }‚ m }ºÓ}¯ËˆÓºä ­ÈÏÒ°Ë {g1 , g 2 , g 3 }  }ÈΩ® mË}ˆº¯ ÓȲº҈°« mº mÏÈ
ÒäÓººÓºÏÓÈӺ䰺ºˆmˈ°ˆmÒÒ°‚¹º¯«ºËÓÓº®ˆ¯º®}º®Ò°Ëã α , β , γ °mºÒäÒ}º

Страницы