試題詳解

109中山電機
Consider the lincar mapping L: V→W. Let Ov and Ow be the zero vectors in V and W, respectively. Which of the following statements are true?
(A) The condition L(v₁) = L(v₂) implies v = V2.
(B) For any w W, there exists v  V such that L(v) = w.
(C) If L is onc-to-one, then L(v) = 0w implies v = 0v.
(D) Ifv₁,v₂, , V_k are linearly independent, L(v₁), L(v₂), ...,L(v_k) are also linearly independent.
(E)The condition c₁v₁+c2v₂+c_kv_k=0vimplies c₁L(v₁)+c₂L(v₂)+⋯+c_kL(v_k)=0w.