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What is Matrix Solutions to Polynomial Equations about?

The document presents a math problem involving finding 2x2 matrices A with real entries that satisfy the polynomial equation A^2 - 2A + 3I = 0, where I is the 2x2 identity matrix. It asks the reader to: (1) Find a matrix A that satisfies the equation by setting A equal to the diagonal matrix λI (2) Show that if A satisfies the equation, so does PAP^-1 for any invertible 2x2 matrix P (3) Find an example of a matrix A with all four entries non-zero (4) Find more examples and argue the equation has infinite

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api-222929991

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EN