12. (10%) Consider the matrix M in (t). It is known that M has four distinct eigenvalues, and let us denote the four corresponding cigenvectors as Which of the following mattices also has as its eigenvectors? (A) (B) (C) (D)(E)

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)

12. (10%) Consider the matrix M in (t). It is known that M has four distinct eigenvalues, and let us denote the four corresponding cigenvectors as Which of the following mattices also has as its eigenvectors?
(A)
(B)
(C)
(D)
(E)

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