Question

用基础解系方程组X1+X2-2X4=-6,4X1-X2-X3-X4=1,3X1-X2-X3=3的全部解

Answer 1

增广矩阵为

[1,1,0,-2,-6; 4,-1,-1,-1,1; 3,-1,-1,0,3]

作行变换得

[1,0,0,-1,-2; 0,1,0,-1,-4; 0,0,1,-2,-5]

所以解为

(x1,x2,x3,x4)=k(1,1,2,1)+(-2,-4,-5,0)

其中k为任意实数