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Math Help - True or False

  1. #1
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    True or False

    Two eigenvectors corresponding to the same eigenvalue must be linear dependent.
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  2. #2
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    I think it is true.
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  3. #3
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    No, it's false. For example, the identity matrix \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix} has 1 as its only eigenvalue. Both [1 0] and [0 1] are eigenvectors corresponding to eigenvalue 1 and are independent.
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