用初等变换求矩阵A=
(11-1
210
1-10)
的逆A-1．
(A，E)= (1 1 -1 1 0 0 2 1 0 0 1 0 1 -1 0 0 0 1) → (1 1 -1 1 0 0 0 -1 2 -2 1 0 0 -2 1 -1 0 1) → (1 1 -1 1 0 0 0 -1 2 -2 1 0 0 0 -3 3 -2 1) → 1 1 -1 1 0 0 0 1 -2 2 -1 0 0 0 1 -1 2/3 -1/3) → (1 0 0 0 1/3 1/3 0 1 0 0 1/3 -2/3 0 0 1 -1 2/3 -1/3) 所以 A-1= (0 1/3 1/3 0 1/3 -2/3 -1 2/3 -1/3)
