求方阵的逆矩阵 3 2 1,3 1 5 ,3 2 3 .
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解: (A,E) =
3 2 1 1 0 0
3 1 5 0 1 0
3 2 3 0 0 1
r2-r1,r3-r1
3 2 1 1 0 0
0 -1 4 -1 1 0
0 0 2 -1 0 1
r1*(1/3),r2*(-1),r3*(1/2)
1 2/3 1/3 1/3 0 0
0 1 -4 1 -1 0
0 0 1 -1/2 0 1/2
r1-(1/3)r3,r2+4r3
1 2/3 0 1/2 0 -1/6
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
r1-(2/3)r2
1 0 0 7/6 2/3 -3/2
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
A^-1 =
7/6 2/3 -3/2
-1 -1 2
-1/2 0 1/2
3 2 1 1 0 0
3 1 5 0 1 0
3 2 3 0 0 1
r2-r1,r3-r1
3 2 1 1 0 0
0 -1 4 -1 1 0
0 0 2 -1 0 1
r1*(1/3),r2*(-1),r3*(1/2)
1 2/3 1/3 1/3 0 0
0 1 -4 1 -1 0
0 0 1 -1/2 0 1/2
r1-(1/3)r3,r2+4r3
1 2/3 0 1/2 0 -1/6
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
r1-(2/3)r2
1 0 0 7/6 2/3 -3/2
0 1 0 -1 -1 2
0 0 1 -1/2 0 1/2
A^-1 =
7/6 2/3 -3/2
-1 -1 2
-1/2 0 1/2
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