System of Differential Equations Defective Matrix Example (Part 2)

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An example of a 2 X 2 system x' = Ax with defective matrix A.
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Thank you for your explanation it was very simple and understandable for review.

Sara-jcxw
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Are 2 by 2 matrices with repeated eigenvalues always defective when they are non-diagonal? I think every diagonal 2 by 2 matrix is diagonalizable with or without repeated eigenvalues.

jacksonmadison