确定a的值,使线性方程组{X1+X2+X3+X4=1,3X1+2X2+X5+X4=0,X2+2X3+2X4=a,5X1+

增广矩阵=
1 1 1 1 1
3 2 1 1 0
0 1 2 2 a
5 4 3 3 2
r2-3r1,r4-5r1
1 1 1 1 1
0 -1 -2 -2 -3
0 1 2 2 a
0 -1 -2 -2 -3
r1+r2,r3+r2,r4-r2,r2*(-1)
1 0 -1 -1 -2
0 1 2 2 3
0 0 0 0 a-3
0 0 0 0 0
所以a=3时方程组有解,通解为 (-2,3,0,0)^T+k1(1,-2,1,0)^T+k2(1,-2,0,1)^T.