複選題14. (10%) Let S = span( B ) be a subspace of the vector space and B is defined as in (t). Consider the following mappings: Choose the correct statement(s) from the following. (A) Both T, and Tz are linear transforms from S to. (B) Ts is a linear transform from S to . (C) The range of T1is a subspace of and its dimension is 2. (D) The range of T2 is a subspace of and its dimension is 2. (E) The range of T3 is a subspace of and its dimension is 2.

複選題15. (10%) For n > 1, let Sn denote the set of all symmetric matrices and Tn denote the set of all skew-symmetric matrices, that is, Tn = {A | A is a n x n matrix such that AT = -A}. Let U be a n x n matrix such that UTU = In. Furthermore, let Wu ={M I M is a n x n matrix such that UTMU is a diagonal matrix}. For a n xn matrix A, let Au denote the unique matrix B in Wu such that is minimized. Choose the correct statement(s) from the following. (A) Sn is a subspace of and its dimension is n. (B) T. is a subspace of and its dimension is n. (C) WU is a subspace of and its dimension is n. (D)(E)

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