試題詳解

15. (5%) Which of the following statements are correct?
(A) A basis for a subspace is a linearly independent subset of the subspace that is as large as possible.
(B) If V is a subspace of dimension k, then every generating set for V contains exactly k vectors.
(C) is any basis for Rⁿ, then there exists a vector v so that v can not be expressed as a linear combination of bi, ba...., bn.
(D) Let T be a linear operator on Rⁿ, and u and V be two bases forRⁿ. Denote [T]_Bas the representative matrix of T with respect to any basis B for Rⁿ. Then, [T]u and [T]v are similar.
(E) If B is a basis for Rⁿ and T is the identity operator on R", then [T]_B = I_n.