[無官方正解]主題課程_線性映射：one to one and onto#107850-阿摩線上測驗
[無官方正解]主題課程_線性映射：one to one and onto#107850
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, , Vk are linearly independent, L(v1), L(v2), ...,L(vk) are also linearly independent.
(E)The condition c1v1+c2v2+ckvk=0vimplies c1L(v1)+c2L(v2)+⋯+ckL(vk)=0w.
(c). Define UP(t)(a polynomil of degree 2 and its standard form is P(t) = a0+ a1t + a2t2),V R3, and T(U) = Find U such that the image under T of Uis [11, 1, -1]T. (7 pts)
(a) (5%) Find a vector u = (ux, uy, uz) such that T(u) - u and.