增广矩阵化简 2 1 -1 1 1 1 2 1 -1 2 1 1 2 1 3

2 1 -1 1 1
1 2 1 -1 2
1 1 2 1 3
r1-2r3,r2-r3
0 -1 -5 -1 -5
0 1 -1 -2 -1
1 1 2 1 3
r1+r2,r3-r2
0 0 -6 -3 -6
0 1 -1 -2 -1
1 0 3 3 4
r1*(-1/6),r2+r1,r3-3r1
0 0 1 1/2 1
0 1 0 -3/2 0
1 0 0 3/2 1
r1r3
1 0 0 3/2 1
0 1 0 -3/2 0
0 0 1 1/2 1
所以,增广矩阵的秩 = 3 = 系数矩阵的秩 < 4 (未知量的个数)
所以方程组有无穷多解
通解为:(1,0,1,0)' + c(-3,3,-1,2)',c 为任意常数