如何求该非齐次方程组的通解
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等式二 - 等式一:
x1 = 3,
方程组变成:
x2+x3-x4=1 等式三
2x2+x3+2x4=-8 等式四
等式三:
x4=1-x2-x3 等式五
代入等式四:
2x2+x3+2(1-x2-x3)=-8
-> -2x2-x3=-10
-> x3=-2x2+10
代入等式五:
x4=1-x2-(-2x2+10)
-> x4=x2-9
综上:
x1 = 3
x3 = -2x2+10
x4 = x2-9
通解应该就是:
x1 = 3
x2 = k
x3 = -2k+10
x4 = k-9
x1 = 3,
方程组变成:
x2+x3-x4=1 等式三
2x2+x3+2x4=-8 等式四
等式三:
x4=1-x2-x3 等式五
代入等式四:
2x2+x3+2(1-x2-x3)=-8
-> -2x2-x3=-10
-> x3=-2x2+10
代入等式五:
x4=1-x2-(-2x2+10)
-> x4=x2-9
综上:
x1 = 3
x3 = -2x2+10
x4 = x2-9
通解应该就是:
x1 = 3
x2 = k
x3 = -2k+10
x4 = k-9
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