证明 线性方程组 (aux+axz++aux)Au=bAu a+a++a)A=b4 amx+an2x2++amxn)An =b4al 在把n个方程依次相加，得 （a14+0141++anu4i)x+(a41+0241+.+0n2A)2+. +(an41+an41++0mAn)xn=(641+b,41++bn4n） 既Dx+0x,+.+0x,=D1 所以 (D0) 上页
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 =
类似 线性方程组 (aux+ax++anx)42 =b42 (a211+22+.+2nXn)A2=b2A2 (nk1+an2X2+.+AmXn）An2=bnAn2 在把n个方程依次相加，得 (a142+0142++0nuA2)x+(a24+0242+.+anmA)x3+ +(anA2+0nA2+.+0nmA)xn=(642+b,42+.+bnA2) 既0x+Dx2+.+0x,=D2 所以 (D0) 类似可求X3,.,x 上页 回
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 12 1 12 2 22 2 1 12 2 12 22 2 2 2 22 2 n n 2 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