X1-X2+X3-X4=1X1-X2-X3+X4=02X1-2X2-4X3+4X4=-1麻烦高人用高斯消元法解下这个方程

Question

X1-X2+X3-X4=1
X1-X2-X3+X4=0
2X1-2X2-4X3+4X4=-1
麻烦高人用高斯消元法解下这个方程

Answer 1

(1)X1-X2+X3-X4=1
(2)X1-X2-X3+X4=0
(3)2X1-2X2-4X3+4X4=-1
(1)-(2),2X3-2X4=1,X3-X4=1/2,X3=X4+1/2,
(1)+(2),2X1-2X4=1,X1-X2=1/2,X1=X2+1/2,
因为
(3)-(2)*2,-2X3+2X4=-1,X3-X4=1/2,
所以方程组的解为
X1=X2+1/2,X3=X4+1/2,
其中X2、X4为任意实数.