Question

线性代数题目，线性方程组，求详细过程～

Answer 1

26.增广矩阵(A,b)=[1-1000a1][01-100a2][001-10a3][0001-1a4][-10001a5]第1,2，3，4行均加到第5行，初等行变换为[1-1000a1][01-100a2][001-10a3][0001-1a4][00000a1++a2+a3+a4+a5]r(A)=4,方程组有解的充要条件是r(A,b)=r(A)=4,则a1++a2+a3+a4+a5=0此时进一步初等行变换为[1000-1a1+a2+a3+a4][0100-1a2+a3+a4][0010-1a3+a4][0001-1a4]方程组化为x1=a1+a2+a3+a4+x5x2=a2+a3+a4+x5x3=a3+a4+x5x4=a4+x5取x5=0,得特解(a1+a2+a3+a4,a2+a3+a4,a3+a4,a4,0)^T导出组为x1=x5x2=x5x3=x5x4=x5得基础解系(1,1,1,1,1)^T则原方程组的通解是x=(a1+a2+a3+a4,a2+a3+a4,a3+a4,a4,0)^T+k(1,1,1,1,1)^T