Question

n元线性方程组AX=b有唯一解的充分必要条件是 ？为什么不是秩A=n

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