問題詳情

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)⋯+

=

.

參考答案

答案：[無官方正解]
難度：計算中-1
書單：沒有書單，新增