求齐次线性方程组x1+x2+x5=0,x1+x2+x3=0,x3+x4+x5=0的通解

X1+X2+X5=0 X1+X2-X3=0 X3+X4+X5=0 解: 系数矩阵 = 1 1 0 0 1 1 1 -1 0 0 0 0 1 1 1 r2-r1 1 1 0 0 1 0 0 -1 0 -1 0 0 1 1 1 r3+r2, r2*(-1) 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 全部解为: c1(-1,1,0,0,0)' + c2(-1,0,-1,0,1