Question

求线性方程组的通解(需要过程)

Answer 1

x1-2x2+4x3=-5,①

2x1+3x2+x3=4,②

3x1+8x2-2x3=13,③

4x1-x2+9x3=-6.④

②-①*2,7x2-7x3=14,x2=x3+2,

③-①*3,14x2-14x3=28,x2=x3+2,

④-①*4,7x2-7x3=14,x2=x3+2.⑤

把⑤代入①,x1-2(x3+2)+4x3=-5,

x1=-2x3-1,

∴（x1,x2,x3)=(-2t-1,t+2,t)=t(-2,1,1)+(-1,2,0).

还可以用增广矩阵解.