当a取何值时,线性方程组{x1+x2-x3=1 2x1+3x2+ax3=3 x1+ax2+3x3=2无解?

问题描述:

当a取何值时,线性方程组{x1+x2-x3=1 2x1+3x2+ax3=3 x1+ax2+3x3=2无解?

1 1 -1 1
2 3 a 3
1 a 3 2
r2-2r1,r3-r1
1 1 -1 1
0 1 a+2 1
0 a-1 4 1
r3 - (a-1)r2
1 1 -1 1
0 1 a+2 1
0 0 -(a-2)(a+3) -(a-2)
当a=-3时,无解
当a=2时,无穷多解
当a!=2且a!=-3时,唯一解