求方程组x1+2x2+x3-2x4=0,x1-x2-5x3+7x4=0,x2+2x3-3x4=0的基础解系和通解

问题描述:

求方程组x1+2x2+x3-2x4=0,x1-x2-5x3+7x4=0,x2+2x3-3x4=0的基础解系和通解

系数矩阵 A =1 2 1 -21 -1 -5 70 1 2 -3r2-r11 2 1 -20 -3 -6 90 1 2 -3r1-2r3,r2+3r31 0 -3 40 0 0 00 1 2 -3基础解系为:a1=(3,-2,1,0)',a2=(4,-3,0,-1)'通解为:c1a1+c2a2,c1,c2 为任意常数.