a为何值时时,线性方程组{2x1+5x2+5x3+4x4=10 x1+2x2+2x3+x4=3 x1+3x2+3x3+3

增广矩阵(A,b)=
2 5 5 4 10
1 2 2 1 3
1 3 3 3 a
r1-2r2,r3-r2
0 1 1 2 4
1 2 2 1 3
0 1 1 2 a-3
r2-2r1,r3-r1
0 1 1 2 4
1 0 0 -3 -5
0 0 0 0 a-7
r1r2
1 0 0 -3 -5
0 1 1 2 4
0 0 0 0 a-7
当a=7时方程组有解且有无穷多解
此时方程组的通解为:(-5,4,0,0)^T+c1(0,-1,1,0)^T+c2(3,-2,0,1)^T