複選題11. (5%) Please pick the statements below that are true. (A) If A and B are m x n matrices and C is an n X p matrix, then (A + B)C = AC + BC. (B) For any matrices A and B, if A is the inverse of BT, then A is the transpose of B-I. (C) An n x n matrix is invertible if and only if its rows are linearly independent. (D) The codomain of any function is contained in its range. (E) for every standard vector e；, then f(v) mg(v) for every v in Rn.

複選題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 = In.

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