試題詳解

3. (5%) Which of the following is true?
(A) Every function from Rⁿto R^m, T : Rⁿ →R^m, has a standard matrix A such that T(x) = Ax for all .
(B) The metrix transformation induced by an m x n matrix A is a linear traneformation.
(C) The image of the zero vector under any linear transformation is the zero vector.
(D) A function T : Rⁿ -→ R^m is uniquely determined by the images of the standard vectors in its domain.
(E) If f is a linear transformation and f(u) = f(v), then u -v.