Print Page - GR9277.098

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) $\lambda_i^3 = +1, i =1,2,3$

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ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน => GRE - Physics => Topic started by: conantee on September 27, 2010, 03:55:07 AM