複選題Which of the following transformations are not linear?(A) S: the map in R3 which rotates points about the x1-axis by an angle π/2.(B) (C) (D) T(ax2+bx+c)-(a+b)x+(b+c)(E)

複選題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, , 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.

複選題
Which of the following transformations are not linear?

(A) S: the map in R³ which rotates points about the x1-axis by an angle π/2.

(B)

(C)

(D) T(ax²+bx+c)-(a+b)x+(b+c)

(E)

相關試題

相關試卷