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arlan- a amlan-2"aga ar-laraja2"- a2 an-3 ana2 a arlan-2a2an-an-2"a arIan-aa2ard an-a1a2 am-3 ana2"ar-2 -(a2,an-∑ 1+x1a2a3…an-1a =anx1x2…xm+xDn=a1x1X2…xm1+xn(an1xx2…xm2+x-D=2) =anx1x2…xn1+xna-1x1X2…Xm2+xnX-D2 =anX1X2…X1+xnan-X1X 2+…+xnxn-1…xa3x1x2+x2xn-1…xxJD anx1x2…xm1+xa1-1X1x2…xn2+…+x1xn1…xa3x1x2+x2xn-…x1x3[(a1+x1)x2+a2x1] (a-1) (a-1) 4D (a-1) (a-1) =(-1)2[(-1)(-2)…(-n){(-1)(-2)…[-(n-1)]}…(-1) =2!3!.,n 3.计算下列n阶行列式(n≥1) +a2 11+ 1- x3 xn x x2-a x3-a x= an-1an-2…a2 1 1 0 1 a -an-1an-2…a3a1-…-an-1an-2a1a2…an-4-an-1a1a2…an-3-a1a2…an-2 =-an-1an-2…a2-an-1an-2…a3a1-…-an-1an-2a1a2…an-4-an-1a1a2…an-3-a1a2…an-2 =-     1 1 2 1 1 ( ... ) n i i n a a a a ③ Dn= n n n n x x x x x x a x a a a a 1 2 3 1 2 1 1 2 3 1 0 0 0 0 0 0 0 0 0                = 1 2 1 1 1 1 ( 1) ( 1) ...        n  n n n n n a x x x x D =anx1x2…xn-1+xnDn-1=anx1x2…xn-1+xn(an-1x1x2…xn-2+xn-1Dn-2) =anx1x2…xn-1+xnan-1x1x2…xn-2+xnxn-1Dn-2 … =anx1x2…xn-1+xnan-1x1x2…xn-2+…+xnxn-1…x4a3x1x2+xnxn-1…x4x3D2 =anx1x2…xn-1+xnan-1x1x2…xn-2+…+xnxn-1…x4a3x1x2+xnxn-1…x4x3[(a1+x1)x2+a2x1] = ... ( ) 1 1 2 1  1 2 1 1      n i n n i i i n x x x x x x x a x x ④Dn+1= 1 1 1 ( 1) ( ) ( 1) ( ) ( 1) ( ) 1 1 1        a a a n a a a n a a a n n n n n n n          = n n n n n n n n a a a a a a n a a a n ( 1) ( 1) ( 1) ( ) ( 1) ( ) 1 1 1 ( 1) 1 1 1 2 ( 1)                   = ( 1) [( 1)( 2) ( )]{( 1)( 2) [ ( 1)]} ( 1) 2 ( 1)            n  n  n n =2!3!...n! 3.计算下列 n 阶行列式(n≥1): ① n a a a a     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1         ② x x x x a x x x a x x x a x a x x a x x x n n n n             1 2 3 1 2 3 1 2 3 1 2 3
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