判断下列非齐次线性方程组是否有解,有解时,求其一般解（1）2x1+3x2-2x3=1 x1-x2+3x3=1 5x1+3x2-x3=3 (2) 3x1+x2+4x3-3x4=2 2x1-3x2+x3-5x4=1 5x1+10x2+2x3-x4=21大哥,
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(1) 增广矩阵=
2 3 -2 11 -1 3 15 3 -1 3r1-2r2,r3-5r2
0 5 -8 -1
1 -1 3 10 8 -16 -2
r3*(1/8),r1-5r3,r2+r3
0 0 2 1/4
1 0 1 3/4
0 1 -2 -1/4
r1*(1/2),r2-r1,r3+2r1
0 0 1 1/8
1 0 0 5/8
0 1 0 0交换行1 0 0 5/8
0 1 0 00 0 1 1/8
方程组有唯一解:(5/8,0,1/8)^T.
增广矩阵 =3 1 4 -3 2
2 -3 1 -5 1
5 10 2 -1 21
r1-r2 (注1)
1 4 3 2 12 -3 1 -5 1
5 10 2 -1 21
r2-2r1,r3-5r1
1 4 3 2 10 -11 -5 -9 -1
0 -10 -13 -11 16
r2-r31 4 3 2 10 -1 8 2 -17
0 -10 -13 -11 16
r1+4r2,r3-10r2
1 0 35 10 -67
0 -1 8 2 -17
0 0 -93 -31 186
r2*(-1),r3*(-1/31)
1 0 35 10 -67
0 1 -8 -2 17
0 0 3 1 -6r1-10r3,r2+2r3 (注2)1 0 5 0 -70 1 -2 0 50 0 3 1 -6方程组的通解为:(-7,5,0,-6)^T+c(-5,2,1,-3)^T.注1 为了避免分数运算,先凑出第1列的公因子注2 同样为了简化运算,想象第3列与第4列交换,自由未知量为x3