求{ 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3}的逆矩阵,

(A,E) =
3 1 1 1 1 0 0 0
1 3 1 1 0 1 0 0
1 1 3 1 0 0 1 0
1 1 1 3 0 0 0 1
r1+r2+r3+r4
6 6 6 6 1 1 1 1
1 3 1 1 0 1 0 0
1 1 3 1 0 0 1 0
1 1 1 3 0 0 0 1
r1*(1/6),ri-r1,i=2,3,4
1 1 1 1 1/6 1/6 1/6 1/6
0 2 0 0 -1/6 5/6 -1/6 -1/6
0 0 2 0 -1/6 -1/6 5/6 -1/6
0 0 0 2 -1/6 -1/6 -1/6 5/6
ri*(1/2),i=2,3,4
r1-r2-r3-r4
1 0 0 0 5/12 -1/12 -1/12 -1/12
0 1 0 0 -1/12 5/12 -1/12 -1/12
0 0 1 0 -1/12 -1/12 5/12 -1/12
0 0 0 1 -1/12 -1/12 -1/12 5/12
A^-1 =
5/12 -1/12 -1/12 -1/12
-1/12 5/12 -1/12 -1/12
-1/12 -1/12 5/12 -1/12
-1/12 -1/12 -1/12 5/12