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    Fundamental Mathematics: Eigenvectors and Matrices

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    1) Find the eigenvectors and eigenvalues of the matrix A. Hence find the matrix P and a diagonal matrix D such that A = P^?1 DP and compute A^100 (see attached).

    2.i) Verify the Cayley-Hamilton theorem for the matrix A.
    ii) Compute the minimal polynomial of a matrix A and decide whether the matrix is diagonalizable or not. The same question for the matrix B (see attached).

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    Solution Summary

    We solve several problems in linear algebra.