лаплас тeоремаси. детерминантнинг хоссалари. детерминантнинг ҳисоблаш усуллари

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1446983309_62109.doc k k i i i j j j m ... ... 2 1 2 1 k k i i i j j j m ... ... 2 1 2 1 ( ) k k k k k k k i i i j j j i i i j j j j j j i i i j j j m m a ... ... .... ... ... ... ,... , 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 det × - = + + + + + + å ÷ ÷ ÷ ÷ ÷ ø ö ç ç ç ç ç è æ = nn n n n n a a a a a a a a a a ..... ..... ..... ..... ..... ..... ..... ' 2 1 2 22 21 1 12 11 ( ) å = + - …

2 1 1 12 11 3 2 1 3 2 1 3 2 1 1 13 12 11 = × = = l l l l l l nn n n in i i in i i n nn n n n in i i i in i i i n a a a a a a a a a a a a a a a a a a a a a a a a a a a a i = + + + + nn n n n in kn i k i k i k in i i i n a a a a a a a a a a a a a a a a a a a a i ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... …

n nn n n nn n n a a a a a a a a a a a a a a a a a a a a a a a a a × × × × = = - = - = + + ... ... 0 0 ... ... ... ... ... 0 ... 1 ... 0 0 ... ... ... ... ... 0 ... 1 ... 0 0 ... ... ... ... ... 0 ... 33 22 11 4 44 3 34 33 22 1 1 11 3 33 2 23 22 11 1 1 2 22 1 12 11 8 2 0 0 0 0 2 0 0 0 0 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - = - - - = - - - ( ) 9 3 3 1 …

n n n n n n n n n n n n n n n n n n n n n = - - - = - - - 2 2 3 2 2 3 2 1 1 3 1 2 ... ... 1 ......... 1 1 ) )...( )( ( n n n n n n x x x x x x x x x x x x ). )...( )( )...( )( )....( )( ( ) ... ( * ) )...( )( )( )...( )( ( ) ... ( * ) )...( )( ( 1 3 4 2 2 3 1 1 3 1 2 4 3 2 2 2 3 1 1 3 1 2 3 2 1 1 3 1 2 - - - - - - - - = = d - - - - - - = = d - - - = n …

d d d d d d d d d d d d d d d d d n n n n n n n n n n n n n n n n n n 1 1 2 2 1 2 1 1 2 1 2 1 2 1 1 1 1 2 1 1 2 1 1 2 2 3 2 2 1 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( .. ) ( ) ( 2 o 2 1 1 6 5 5 ... 0 0 0 0 ... 5 2 0 0 ... 3 5 2 3 2 5 5 ... 0 0 0 0 ... 5 2 0 0 ... 3 5 2 0 ... 0 0 3 2 5 ... 0 0 0 . .......... 0 ... 5 2 0 0 ... 3 5 …

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1446983309_62109.doc k k i i i j j j m ... ... 2 1 2 1 k k i i i j j j m ... ... 2 1 2 1 ( ) k k k k k k k i i i j j j i i i j j j j j j i i i j j j m m a ... ... .... ... ... ... ,... , 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 det × - = + + + + + + å ÷ ÷ ÷ ÷ ÷ ø ö ç ç ç ç ç è æ = nn n n n n a a …

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