(a) A 3x3 matrix A has an eigenvalue 1 and a corresponding eigenvector [1, -1, 1]. The matrix A has also another eigenvalue -2 that has an algebraic multiplicity 2 and the corresponding eigenvectors [-1, 1, 0] and [-1, 0, 1]. Show how to determine the matrix A. (b) Consider the matrix A = [1 2; 4 3]. Find the eigenpairs of the matrix A.
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