題組內容

5. Let A be an m x n matrix, X∈Rn denote a vector, and L(x) = Ax be a linear transformation. row(A), col(A), and N(A) respectively represent the row space, the column space, and the null space of A. rank(A) and nullity(A) respectively represent the rank and nullity of A. kernel(L) and range(L) respectively represent the kernel and the range of L. If V is a vector space/subspace, dim(V) denotes the dimension of V.Consider the following statements: 

(A) row(A) = Rn. 
(B) col(A) = Rm. 
(C) dim(col(A)) ＜m. 
(D) Ax = 0 has infinite solutions. 
(E) Ax = 0 has exactly one solution. 
(F) Ax = 0 has no solutions. 
(G) Ax = 0 is an inconsistent system. 
(H) Ax = 0 is a consistent system. 
(I)N(A)=⌀. 
(J) rank(A) =m. 
(K) nullity(A) = m. 
(L) kernel(L) = Rn. 
(M)63f5e32b0f2d1.jpg
(N) AAT is not symmetric.

(d) (2 points) What does the statement (L) imply about L?