问ab取何值时线性方程组（x1+ax2+x3=3,x1+2ax2+x3=4,x1+x2+bx3=4)有唯一解,无解,

Question

问ab取何值时线性方程组（x1+ax2+x3=3,x1+2ax2+x3=4,x1+x2+bx3=4)有唯一解,无解,

Answer 1

增广矩阵（A,b)=
1 a 1 3
1 2a 1 4
1 1 b 4
初等行变化~
1 a 1 3
0 a 0 1
0 1-a b-1 1
1 a 1 3
0 a 0 1
0 1 b-1 2
1 a 1 3
0 1 b-1 2
0 0 a(1-b) 1-2a
若方程有唯一解,则r(A)=r(A,b)=3,故detA=a(1-b)不为零,1-2a不为零,所以a≠0,a≠1/2且b≠1
若方程无解,则r(A)