增广矩阵 =
1 1 1 1 1 1
3 2 1 1 -3 c
0 1 2 2 6 3
5 4 3 3 -1 d
r2-3r1,r4-5r1
1 1 1 1 1 1
0 -1 -2 -2 -6 c-3
0 1 2 2 6 3
0 -1 -2 -2 -6 d-5
r1+r2,r3+r2,r4-r2,r2*(-1)
1 0 -1 -1 -5 c-2
0 1 2 2 6 3-c
0 0 0 0 0 c
0 0 0 0 0 d-c-2
所以 c=0,d=2 时有解.此时增广矩阵化为
1 0 -1 -1 -5 -2
0 1 2 2 6 3
0 0 0 0 0 0
0 0 0 0 0 0
方程组的通解为:(-2,3,0,0,0)'+c1(1,-2,1,0,0)'+c2(1,-2,0,1,0)'+c3(5,-6,0,0,1)'