Question

2X1+X2-X3+X4=1;X1+2X2+X3-X4=2;X1+X2+2X3+X4=3.求出该方程的通解.

Answer 1

2x1+x2-x3+x4=1……①

x1+2x2+x3-x4=2……②

x1+x2+2x3+x4=3……③

①+②得,3x1+3x2=0,∴x2=-x1……④

②+③得,2x1+3x2+3x3=0……⑤

把④代人⑤得,-x1+3x3=0,∴x3=1/3x1……⑥

把④⑥代人①得,2x1-x1-1/3x1+x4=1,解得x4=1-2/3x1

设x1=3t,

则通解为：(3t,-3t,t,1-2t)