Homework Help for Statistics (page 55)
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3. Suppose that 2 and -5 are the only eigenvalues of the matrix A. Which of the following statements is true? A) 21 - A is invertible, and there is a nontrivial solution to Av = -5v. B) 21 - A is not invertible, and there is a nontrivial solution to Av = -5v. C) det(21 + A) = det(51 – A) = 0. D) det(21 + A) = 0, and there is a nontrivial solution to (51 – A)v = 0.
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