解方程组(x1+2x2+2x3+x4=0,2x1+x2-2x3-2x4=0,x1-x2-4x3-3x4=0)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/06/06 11:34:47

x1+2x2+2x3+x4=0 (1)
2x1+x2-2x3-2x4=0 (2)
x1-x2-4x3-3x4=0 (3)
(2)-(3)
x1+2x2+2x3+x4=0 = equation (1)
rank of system of equations = 2
(1)+(2)
3x1+3x2+3x4=0
x4=-(x1+x2)
from (1)
x1+2x2+2x3-(x1+x2)=0
x3 = -x2/2
solution of system of equations
(x1,x2,x3,x4) = (m,n,-n/2,-(m+n) ) where m,n is a constant

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