Question

n元非齐次线性方程组AX=b有唯一解的充分必要条件

Answer 1

n元线性方程组ax=b有唯一解的充分必要条件是
r(a)
=
r(a,b)
=
n
r(a)
=
n
并不能保证
r(a)
=
r(a,b)
比如
增广矩阵
=
1
1
1
0
1
1
0
0
1
r(a)=2,
r(a,b)=3