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Title: GR9277.098
Post by: conantee on September 27, 2010, 03:55:07 AM
98. The matrix A = \begin{bmatrix}0&1&0 \cr 0&0&1 \cr 1&0&0  \end{bmatrix} has three eigenvalues \lambda_i defined by Av_i = \lambda_i v_i. Which of the following statements is NOT true?
(A) \lambda_1 + \lambda_2 + \lambda_3 = 0
(B) \lambda_1, \lambda_2, and \lambda_3 are all real numbers.
(C) \lambda_2 \lambda_3 = +1 for some pair of roots.
(D) \lambda_1 \lambda_2 +\lambda_2 \lambda_3 + \lambda_3 \lambda_1 =0
(E) \lambda_i^3 = +1, i =1,2,3