試題詳解

20.Consider the linear mapping L:V - W. Let be the zero vectors in V and W, respectively. Which of the following statements are true?
(A) The condition L(V₁) = L(V₂) implies V₁ = V₂.
(B) For any w ∈ W, there exists v ∈ V such that L(V) = W.
(C) If L is one-to-one, then L(V) = impliesv =
(D) IfV₁,V₂,..., are linearly independent, L(V₁), L(V₂),.., are also linearly independent.
(E) The condition G₁V₁:+C₂V₂+...+= implies c₁L(V₁)+c₂L(V₂)+⋯..+=