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) impliesV₁ = 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) = 0w implies v = Ov.
(D) If V₁,V₂,..., are linearly independent, L(V₁), L(V₂),.., are also linearly independent.

(E) The condition C₁V₁+C₂V₂+..+=implies c₁L(V₁)+c₂L(V₂)⋯+=.