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    Let A be a matrix,  a real eigenvalue of A, and v the associated eigen-vector.

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    Let A be an nxn matrix, λ a real eigenvalue, v the associated eigenvector. Show that A^k v= λ^k v.
    Use this to show e^At v= e^λt v. Use this to show that the line through the origin consists of two solutions to x'=Ax.

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    Solution Summary

    Parametrize the two halves of this line.