Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 314 стр.

UptoLike

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒ˰}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
¯wããÒ¹°ºÒ
|¹¯ËËãËÓÒË
¯
ºm˯²Óº° ÏÈÈmÈËäÈ«mÓË}ºº¯º®º¯ºÓº¯äÒ¯ºmÈÓÓº®°Ò°ËäË}º
º¯ÒÓÈ}ÈÓºÓÒ˰}Òä¯ÈmÓËÓÒËämÒÈ
x
a
y
b
z
c
abc
2
2
2
2
2
2
1000
++= >>>
:,,
ÓÈÏ©mÈË°«ëssqwxvqlvu
vmº®°mÈªããÒ¹°ºÒÈ
°wããÒ¹°ºÒº¯ÈÓÒËÓÓÈ« ¹ºm˯²Óº° ¹º°}ºã} ÒÏ ˺ }ÈÓºÓÒ˰}ºº
¯ÈmÓËÓÒ«°ãËËº
|| ;|| ;||xaybzc≤≤

°wããÒ¹°ºÒºãÈÈË
ËÓ¯ÈãÓº®°ÒääË¯ÒË®ºÓº°ÒËãÓºÓÈÈãÈ}ºº¯ÒÓÈ
º°Ëmº®°ÒääË¯ÒË®ºÓº°ÒËãÓº}ºº¯ÒÓÈÓ©²º°Ë®
¹ãº°}º°Óº®°ÒääË¯ÒË®ºÓº°ÒËãÓº}ºº¯ÒÓÈÓ©²¹ãº°}º°Ë®
°{°ËËÓÒÒªããÒ¹°ºÒÈ¹ãº°}º°
º¯ººÓÈãÓº®ãº®ÒÏº°Ë®}º
º¯ÒÓÈ ¹ºãÈË°« ëssqwx sÈ
¹¯Òä˯ ¯È°°äÈ¯ÒmÈ« °Ë}
¹ãº°}º°
zz=
0
Ë
zc
0
<
¹ºã
ÈËä °ãËËË ¯ÈmÓËÓÒË ãÒÓÒÒ
°ËËÓÒ«
=
=
+
0
2
2
2
0
2
2
2
2
0
2
1
)1()1(
zz
c
z
b
y
c
z
a
x

«mã«Ë®°« ªããÒ¹°ºä cÒ°
¯
x

z
èqxytvr¯
y
¯wããÒ¹Ò˰}Ò®¹È¯ÈºãºÒ
|¹¯ËËãËÓÒË
¯
ºm˯²Óº° ÏÈÈmÈËäÈ«mÓË}ºº¯º®º¯ºÓº¯äÒ¯ºmÈÓÓº®°Ò°ËäË}º
º¯ÒÓÈ }ÈÓºÓÒ˰}Òä ¯ÈmÓËÓÒËä È
x
a
y
b
za b
2
2
2
2
200
+= >>
;,

ÓÈÏ©mÈË°«ëssqwzq·nxrquwjéjivsvqlvu
 Ë }  Ò Ò   } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈Ò˰}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



¯wããÒ¹°ºÒ
            
            
            
 |¹¯ËËãËÓÒË            ºm˯²Óº°ˆ ÏÈÈmÈËäÈ«mÓË}ºˆº¯º®º¯ˆºÓº¯äÒ¯ºmÈÓÓº®°Ò°ˆËäË}º
 ¯              º¯ÒÓȈ}ÈÓºÓÒ˰}Ò䂯ÈmÓËÓÒËämÒÈ
                                  x2       y2       z2
                                       +        +        = 1 : a > 0, b > 0, c > 0 ÓÈÏ©mÈˈ°«ëssqwxvqlvu
                                  a2       b2       c2
            
            
vmº®°ˆmȪããÒ¹°ºÒÈ
          
          
 °wããÒ¹°ºÒ  º¯ÈÓÒËÓÓÈ« ¹ºm˯²Óº°ˆ  ¹º°}ºã }‚ ÒÏ Ëº }ÈÓºÓÒ˰}ºº
     ‚¯ÈmÓËÓÒ«°ãË‚ˈˆº | x | ≤ a ; | y | ≤ b ; | z | ≤ c 
              
 °wããÒ¹°ºÒº­ãÈÈˈ
         Ëӈ¯Èã Óº®°Òääˈ¯ÒË®ºˆÓº°ÒˆËã ÓºÓÈÈãÈ}ºº¯ÒÓȈ
         º°Ëmº®°Òääˈ¯ÒË®ºˆÓº°ÒˆËã Óº}ºº¯ÒÓȈө²º°Ë®
         ¹ãº°}º°ˆÓº®°Òääˈ¯ÒË®ºˆÓº°ÒˆËã Óº}ºº¯ÒÓȈө²¹ãº°}º°ˆË®
            
 °{°ËËÓÒÒªããÒ¹°ºÒȹ㺰}º°ˆ                    z      
     º¯ˆººÓÈã Óº®ã ­º®ÒϺ°Ë®}º                                                         
     º¯ÒÓȈ ¹ºã‚Èˈ°« ëssqwx sÈ                                                      
     ¹¯Òä˯ ¯È°°äȈ¯ÒmÈ« °Ë}‚‚                                                          
                                                                                             
     ¹ãº°}º°ˆ  z = z0 Ë z0 < c ¹ºã‚                                                 
     ÈËä °ãË‚ ËË ‚¯ÈmÓËÓÒË ãÒÓÒÒ                                                      
     °ËËÓÒ«                                                                                
                                                                                            
                 2               2                                                          
                x               y
                        +              =1                                                   
                   z 2
                                    z 2                                                      
        (a 1 − 0 ) 2 (b 1 − 0 ) 2         
                                                                                             y
                  c  2
                                   c  2
                                                  
                      z = z0
                                                  x
                           
                                                                                           
     «mã« Ë®°«            ªããÒ¹°ºä      cÒ°                        èqxytvr¯
     ¯ 
          
          
          
            

¯wããÒ¹ˆÒ˰}Ò®¹È¯È­ºãºÒ
            
            
            

 |¹¯ËËãËÓÒË            ºm˯²Óº°ˆ ÏÈÈmÈËäÈ«mÓË}ºˆº¯º®º¯ˆºÓº¯äÒ¯ºmÈÓÓº®°Ò°ˆËäË}º
 ¯
                                                                                                    x2       y2
                         º¯ÒÓȈ }ÈÓºÓÒ˰}Òä ‚¯ÈmÓËÓÒËä mÒÈ                                        +        = 2 z ; a > 0, b > 0 
                                                                                                    a2       b2
                         ÓÈÏ©mÈˈ°«ëssqwzq·nxrquwjéjivsvqlvu