@少本T子大￥ 证明 线性方程组 (aux+arx2++ax)Au=b4u (a21k1+a2x2+.+mXn)A1=b2A1 anx+an2x2++amxn)An bnAu 在把n个方程依次相加，得 (au41+a141++0nm4n小x+(2A1+041+.+an2An)x+ +autai++am)=br++An) 既 Dx+0x++0x=D 所以 5(D*) 上页 回
证明 在把 n 个方程依次相加，得 11 1 12 2 1 1 21 1 22 2 2 2 1 1 2 2 n n n n n n nn n n a x a x a x b a x a x a x b a x a x a x b + + + = + + + = + + + = 线性方程组 (a x a x a x A b A 11 1 12 2 1 11 1 11 + + + = n n ) (a x a x a x A b A 21 1 22 2 2 21 2 21 + + + = n n ) (a x a x a x A b A n n nn n n n n 1 1 2 2 1 1 + + + = ) ( ) ( ) ( ) ( ) 11 11 21 1 12 11 22 21 2 1 2 1 11 2 21 1 1 11 21 1 1 1 2 21 n n n n nn n n n n n n x a A a A a A x a A a A a A x b A b A b a A A a A a A + + + + + + + + + = + + + + + + 既 ( ) 1 2 1 11 2 21 1 0 0 n n n Dx x x b A b A b + + + = + + + D1 A ( ) 1 1 0 D x D D 所以 =
G心山东理上大￥ 类似线性方程组 (au+apxz++anx)42=b42 (a211+0z2++42mn)A2=b2A22 人ani七1+am2x32+.+0nmxn)A2=bnA2 在把n个方程依次相加，得 (4n42+014nt+0uAa)x+(a242+a42++an4)x+ +(anA4+0nA2+.+0nA2)x.=(b42+b42+.+bn4n2） 既 Ox+Dx,++Ox=D2 所以 (（D≠0)类似可求 X3
类似 在把 n 个方程依次相加，得 11 1 12 2 1 1 21 1 22 2 2 2 1 1 2 2 n n n n n n nn n n a x a x a x b a x a x a x b a x a x a x b + + + = + + + = + + + = 线性方程组 (a x a x a x A b A 11 1 12 2 1 12 1 12 + + + = n n ) (a x a x a x A b A 21 1 22 2 2 22 2 22 + + + = n n ) (a x a x a x A b A n n nn n n n n 1 1 2 2 2 2 + + + = ) ( ) ( ) ( ) ( ) 11 12 21 22 1 2 1 2 1 12 2 22 2 12 12 22 22 1 12 2 22 2 2 2 n n n n nn n n n n n n a A a A a A x x a A a A a A x b A b A b A + + + + + a A a A a A + + + + = + + + + + + 既 ( ) 1 2 1 12 2 22 2 0 0 n n n x x x b A A b + + + = + + + D D2 b A ( ) 2 2 0 D x D D 所以 = 类似可求 3 , , . n x x