11. (10%) Consider a matrixWhich of the following is an eigenvalue of this matrix M? (A)1 (B)-3 (C)9 (D) -1+2j (E) -1+4j

11. (10%) Consider a matrix
Which of the following is an eigenvalue of this matrix M?
(A)1
(B)-3
(C)9
(D) -1+2j
(E) -1+4j

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Terry Tung

2022/01/11

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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)

11. (10%) Consider a matrixWhich of the following is an eigenvalue of this matrix M? (A)1 (B)-3 (C)9 (D) -1+2j (E) -1+4j

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11. (10%) Consider a matrix
Which of the following is an eigenvalue of this matrix M?
(A)1
(B)-3
(C)9
(D) -1+2j
(E) -1+4j