求非齐次线性方程组通解
问题描述：
求非齐次线性方程组通解
X1+X2+X3+3X4+X5=7
3X1+X2+2X3+X4-3X5=-2
2X2+X3+2X4+6X5=23
8X1+3X2+4X3+3X4-X5=12
答
第3个方程 2X2+X3+2X4+6X5=23 没错吧解: 增广矩阵 =1113173121 -3 -202126 238343 -1 12 r2-3r1,r4-8r11113170 -2 -1 -8 -6 -2302126 230 -5 -4 -21 -9 -44 r3+r2,r4-2r21113170 -2 -1 -8 -6 -23000 -6000 -1 -2 -532 r3*(-1/6),r1-3r3,r2+8r3,r4+5r31110170 -2 -10 -6 -230001000 -1 -2032 r1+r4,r2+2r4,r4*(-1)10 -10490030 -12 -270001000120 -3 -2 r2*(1/3),r1+r2,r4-2r21000000010 -4 -900010001005 16 交换行10000001005 160010 -4 -9000100 通解为: (0,16,-9,0,0)^T+c(0,-5,4,0,1)^T.