Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 128 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
cÈÏËã
vjvplhjspqshtck{spsjq
|¹¯ËËãÒËãÒ
cȰ°äº¯Òä äÓºÎ˰mº °º°º«ËË ÒÏ ÓÈ¯ÈãÓ©² Ò°Ëã
1,2,3,...,n
 rËä
ººÏÓÈÈ wnénxzjtvkrqªÒ²Ò°Ëãº˰ ¹º°ã˺mÈËãÓ ÏȹҰªÒ²Ò°Ëã m
ÓË}ºº¯ºä¹º¯«}ËËÏ¹ºmº¯ËÓÒ®}È}
{, , ,..., }kkk k
n
123
sȹºäÓÒäº¹ºãÓºËÒ°ãº
È}Ò²¯ÈÏãÒÓ©²¹Ë¯Ë°ÈÓºmº}¯ÈmÓº
n!

|¹¯ËËãËÓÒË

rËäºmº¯Ò ºÒ°ãÈ
k
i
Ò
k
j
º¯ÈÏ m¹Ë¯Ë°ÈÓºm}Ë inxwvé¹
lvr tjéy¡ntqn wvé¹lrj ÒãÒ qtknéxqí ˰ãÒ ¹¯Ò
i<j
ÒäËË ä˰º
kk
ij
>

ºãÓºË Ò°ãº ˰¹º¯«}ºm m ¹Ë¯Ë°ÈÓºm}Ë
{, , ,..., }kkk k
n
123
Ëä ººÏÓÈÈ
ï( , , ,..., )kkk k
n
123
sȹ¯Òä˯
ï (,,,)3142 3=

°ÈÓÈ}mȯÈÓÈ«äÈ¯ÒÈ
Aijn
n
n
n
nn n nn
ij
===
ααα α
ααα α
ααα α
ααα α
α
11 12 13 1
21 22 23 2
31 32 33 3
123
1
...
...
...
... ... ... ... ...
...
;, [,]

|¹¯ËËãËÓÒË

bnznéuqtjtzvu ÒãÒ vwénlnsqznsnu }mȯÈÓº® äÈ¯Ò©
A
¯ÈÏä˯È
n
[
n
ÓÈÏ©mÈË°«Ò°ãº
det
A
¹ºãÈËäºË¹ºÁº¯äãË
 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










cÈÏËã
vjv‘plhjspqshtck{spsjq




|¹¯ËËã҈ËãÒ
       
       
       
       cȰ°äºˆ¯Òä äÓºÎ˰ˆmº °º°ˆº«ËË ÒÏ ÓȈ‚¯Èã Ó©² Ò°Ëã 1,2,3, ..., n  r‚Ëä
º­ºÏÓÈȈ  wnénxzjtvkrq ªˆÒ² Ò°Ëã ˆº ˰ˆ  ¹º°ã˺mȈËã ӂ  ÏȹҰ  ªˆÒ² Ò°Ëã m
ÓË}ºˆº¯ºä¹º¯«}Ë­ËϹºmˆº¯ËÓÒ® }È} {k1 , k 2 , k 3 ,..., k n } sȹºäÓÒ䈺¹ºãÓºËÒ°ãº
ˆÈ}Ò²¯ÈÏãÒÓ©²¹Ë¯Ë°ˆÈÓºmº}¯ÈmÓºn!
             
             
             
 |¹¯ËËãËÓÒË             r‚Ëä ºmº¯Òˆ  ˆº Ò°ãÈ k i  Ò k j  º­¯Èς ˆ m ¹Ë¯Ë°ˆÈÓºm}Ë inxwvé¹
 
                          lvr tjéy¡ntqn wvé¹lrj ÒãÒ qtknéxqí  ˰ãÒ ¹¯Ò i k j 
             
             
             
             ºãÓºË Ò°ãº ­Ë°¹º¯«}ºm m ¹Ë¯Ë°ˆÈÓºm}Ë {k1 , k 2 , k 3 ,..., k n }  ­‚Ëä º­ºÏÓÈȈ 
 ï( k 1 , k 2 , k 3 ,..., k n ) sȹ¯Òä˯ ï(3,1,4,2) = 3 
             
             
             ‚°ˆ ÈÓÈ}mȯȈÓÈ«äȈ¯ÒÈ
             
             
                                     α11           α12      α13      ... α1n
                                     α 21          α 22     α 23     ... α 2 n
                                 A = α 31          α 32     α 33     ... α 3n = αij ; i , j = [1, n ] 
                                      ...           ...      ...     ... ...
                                     α n1          α n2     α n3     ... α nn
            
            
    |¹¯ËËãËÓÒË         bnznéuqtjtzvu                   ÒãÒ vwénlnsqznsnu  }mȯȈӺ® äȈ¯Ò©                                        A 
    
                         ¯ÈÏä˯Èn[nÓÈÏ©mÈˈ°«Ò°ãº det A ¹ºã‚ÈËäºË¹ºÁº¯ä‚ãË