增广矩阵 =
1 1 -2 3 0
2 1 -6 4 -1
3 2 k1 7 -1
1 -1 -6 -1 k2
r2-r1-r2,r2-2r1,r4-r1
1 1 -2 3 0
0 -1 -2 -2 -1
0 0 k1+8 0 0
0 -2 -4 -4 k2
r1+r2,r4-2r2,r2*(-1)
1 0 -4 1 -1
0 1 2 2 1
0 0 k1+8 0 0
0 0 0 0 k2+2
当k2≠-2时,方程组无解 (这叫做非零的尾巴,有它就无解)
当k2=-2时,方程组有无穷多解.
此时再分两种情况:
(1)当k1≠-8时,所有解为 (-1,1,0,0)'+c(1,2,0,-1)'.
(2)当k1=-8时,所有解为 (-1,1,0,0)'+c1(4,-2,1,0)+c2(1,2,0,-1)'.