求非齐次线性方程组的通解：2x1+x2-x3-x4=1;2x1+x2+x3-x4=1;4x1+2x2+x3-2x4=2
问题描述：
求非齐次线性方程组的通解：2x1+x2-x3-x4=1;2x1+x2+x3-x4=1;4x1+2x2+x3-2x4=2
答
增广矩阵=2 1 -1 -1 12 1 1 -1 14 2 1 -2 2r2-r1,r3-2r12 1 -1 -1 10 0 2 0 00 0 3 0 0r2*(1/2).r1+r2,r3-3r22 1 0 -1 10 0 1 0 00 0 0 0 0通解为:(0,1,0,0)^T+c1(1,-2,0,0)^T+c2(0,1,0,1)^T*未知量x1, x4 分别取 (0,0), (1,0), (0,1)