求非其次线性方程组的通解X1+X2+X3+X4+X5=7你好刘老师,X1+X2+X3+X4+X5=73X1+2X2+X3+X4-3X5=-2X2+2X3+2X4+6X5=235X1+4X2-3X3+3X4-X5=12这得出X1=-16+X4+ 5X5X2=23-2X4- 6X5X3=0给的参考答案得出K1=(1,-2,0,1,0),K2=(-5,-6,0,0,1)可是我

Question

求非其次线性方程组的通解X1+X2+X3+X4+X5=7
你好刘老师,
X1+X2+X3+X4+X5=7
3X1+2X2+X3+X4-3X5=-2
X2+2X3+2X4+6X5=23
5X1+4X2-3X3+3X4-X5=12
这得出
X1=-16+X4+ 5X5
X2=23-2X4- 6X5
X3=0
给的参考答案得出K1=(1,-2,0,1,0),K2=(-5,-6,0,0,1)
可是我按照X4,X5分别为1,0求出来的是K1=(-15,21,0,1,0) K2=(-11,17,0,0,1) 烦请你看下,

Answer 1

求基础解系时应该令常数项为0
即
X1=X4+ 5X5
X2=-2X4- 6X5
X3=0