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Matrix Theory: We apply the minimal polynomial to matrix computations. For a given real 3x3 matrix A, we find the characteristic and minimal polynomials and evaluate p(A) and q(A) for p(x) = x^3 + x^2 + 1 and q(x) = x^2 + 1. Then we apply Bezout's Identity to find matrices X and Y such that Xp(A) + Yq(A) = I.
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