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Eigenvalue statements help

  1. Dec 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Let A and B be n x n matrices, where B is invertible. Suppose that 2 is an eigenvalue of A, and −2 is an eigenvalue of B. Find ALL true statements below.

    A. −4 is an eigenvalue of AB
    B. 16 is an eigenvalue of A^3+A+6I
    C. 4 is an eigenvalue of A+A(Transpose)
    D. 2 is an eigenvalue of A(Transpose)
    E. 2 is an eigenvalue of B^(−1)AB
    F. None of the above

    3. The attempt at a solution

    I'm not sure how to do this question, so can anyone show me the correct way to solve this?
    I picked 2 random matrices for A and B that fit the given description and tried all of the operations. Only A,B,D,E worked, but it's the wrong answer.

    Can anyone help me?

    Last edited: Dec 4, 2009
  2. jcsd
  3. Dec 4, 2009 #2


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    Homework Helper

    Re: Eigenvalues

    see if these help
    A) can you think of a counter example with diagonal matricies?
    B,C,D) try writing the determinsitic equation and see what you get...
    E) do you know about similar matricies?
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