用初等矩阵行变换解下题,求大神

增广矩阵=
1 1 2 4 3
3 1 6 2 3
-1 2 -2 1 1
r2-3r1,r3+1
1 1 2 4 3
0 -2 0 -10 -6
0 3 0 5 4
r2*(-1/2),r1-r2,r3-3r2
1 0 2 -1 0
0 1 0 5 3
0 0 0 -10 -5
r3*(-1/10),r1+r3,r2-5r3
1 0 2 0 1/2
0 1 0 0 1/2
0 0 0 1 1/2
方程组的通解为 (1/2,1/2,0,1/2)^T + k(-2,0,1,0)^T