(Solution) - Write down a real matrix that has a Eigenvalues 1 3 -(2025 Original AI-Free Solution)

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Write down a real matrix that has
(a) Eigenvalues -1, 3 and corresponding eigenvectors

(b) Eigenvalues 0, 2, -2 and associated eigenvecors
(c) An eigenvalue of 3 and corresponding eigenvectors
(d) An eigenvalue -1 + 2i and corresponding eigenvector
(e) An eigenvalue -2 and corresponding eigenvecor
(f) An eigenvalue 3 + i and corresponding eigenvector