98年國立中正大學電機所(計算機組)線性代數線上測驗

2.
(A): (a) If E is an m × m elementary matrix, then A and EA must have the same nullspace
(B): (b) If E is an m × m elementary matrix, then A and EA must have the same row space.
(C): (c) The row space and nullspace of an invertible matrix A are the same.
(D): (d) If E is an n × n elementary matrix, then A and AE must have the same column space
(E): (e) If Ax = b does not have any solutions, then b is not in the column space of A.