设线性方程组x1+x2-x3=-1 2x1+kx2-2x3=0 kx1+2x2+x3=k,问k为何值时方程组有唯一解,无解,有无穷多解

问题描述:

设线性方程组x1+x2-x3=-1 2x1+kx2-2x3=0 kx1+2x2+x3=k,问k为何值时方程组有唯一解,无解,有无穷多解

一式-1/2*二式得:(k/2-1)x2=1.故k=2时方程组无解一式+3式得:(k+1)x1+3x2=k-1.k2时x2=2/(k-2).代入得(k-2)(k+1)x1=(k+1)(k-4).故k=-1时方程组无穷多解,为x1=c,x2=-2/3,x3=c+1/3,c∈Rk-1且k2时,方程组唯一解,...