由 Ax = b,得 x = A^(-1)b.
(A,E) =
[1 1 -1 1 0 0]
[1 -2 -1 0 1 0]
[-2 -3 -1 0 0 1]
初等变换为
[1 1 -1 1 0 0]
[0 -3 0 -1 1 0]
[0 -1 -3 2 0 1]
初等变换为
[1 1 -1 1 0 0]
[0 1 3 -2 0 -1]
[0 0 9 -7 1 -3]
初等变换为
[1 1 0 2/9 1/9 -1/3]
[0 1 0 1/3 -1/3 0]
[0 0 1 -7/9 1/9 -1/3]
初等变换为
[1 0 0 -1/9 4/9 -1/3]
[0 1 0 1/3 -1/3 0]
[0 0 1 -7/9 1/9 -1/3]
则 A^(-1) =
[-1/9 4/9 -1/3]
[ 1/3 -1/3 0]
[-7/9 1/9 -1/3]
x = A^(-1)b = (4/9,-1/3,-8/9)^T.