1:b10 1;0b, -00:b b10 0:0b 0 1:00 0:00 tbb2…bn=b1b2…b1+1+ 6, b, 例3设A=-11 满足AX=A-+2X,求X 解并项:(A-2E)X=A 左乘A:I(det4)E-24X=E 计算:cetA=4 X=(4E-2A)-2 (2E-A)=011 10 例4求解Ax=b,A=111,b= 11a1 解A=1x11:4→1-4元-100:-1 111:a 1-0元-10:2 →-1100:1奇|2+2001:-(4+1) 1010:元+1 1010:+1 1100:1 x2=1+x1 (1)元≠1:同解方程组为{x3=(+1)+x1 x4=-(1+1)-(元+2)x12 n n b b b a a a         1 0 0 1 0 0 1 0 0 1 2 1 1 2 − − − = n n b b b t a a a         0 0 0 0 0 0 0 0 0 2 1 1 2 = b b bn b b bn = t 1 2  = 1 2          + + + + n n b a b a b a  2 2 1 1 1 例 3 设           − − − = 1 1 1 1 1 1 1 1 1 A 满足 A X A 2X 1 = +  − , 求 X ． 解 并项： 1 ( 2 )  − A − E X = A 左乘 A ： [(detA)E − 2A]X = E 计算： detA = 4 1 1 (2 ) 2 1 (4 2 ) − − X = E − A = E − A           = 1 0 1 0 1 1 1 1 0 4 1 例 4 求解 Ax = b,           = 1 1 1 1 1 1 1 1 1    A ,           = 2 1  b  解           = 2 1 1 1 1 1 1 1 1 1 1 ~      A           − − − → − − − 1 0 1 0 1 1 1 0 0 1 1 1 1 1 2        行           − + → −  1 0 1 0 1 1 1 0 0 1 1 1 1 1 1    行           − − + + − + → 1 1 0 0 1 1 0 1 0 1 2 0 0 1 ( 1)    行 (1)   1 ：同解方程组为      = − + − + = + + = + 4 1 3 1 2 1 ( 1) ( 2) ( 1) 1 x x x x x x   