解非线性方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0

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解非线性方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0

解非线性方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0
解非线性方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0

解非线性方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0
这明明是一个齐次线性方程组.
[1 2 2 1 ] [1 2 2 1 ] [1 2 2 1] [1 2 2 1] [1 0 -2 -5/3]
[2 1 -2 -2 ]→ [0 -3 -6 -4 ] → [0 3 6 4]→[0 1 2 4/3]→[0 1 2 4/3]
[1 -1 -4 -3 ] [0 -3 -6 -4 ] [0 0 0 0 ] [0 0 0 0] [0 0 0 0 ]
取 x3=k1 x4=k2
则 x1=2k1+5/3k2
x2=-2k1-4/3k2
通解为:x=k1(2,5/3,1,0)T +k2(-2,-4/3,0,1)T

1 2 2 1 1 2 2 1 1 2 2 1
2 1 -2 -2 = 0 -3 -6 -4 = 0 3 6 4
1 -1 -4 -3 0 -3 -6 -4 0 0 0 0
x1-4+2=0
3x2+6=0
x3=1 x4=0 x2=-2 x1=2
x=C(2,-2,1,0)T

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