Suppose that the 2 x 2 matrix A has eigenvalues 1 1 and 2 1 with eigenvectors v1 (3, 4) and v2 (5,7), respectively Find the matrix A and the powers A 99 and A 100

Question: Suppose that the 2 x 2 matrix A has eigenvalues 1 = 1 and 2 = -1 with eigenvectors v1 = (3, 4)

Suppose that the 2 x 2 matrix A has eigenvalues λ₁ = 1 and λ₂ = -1 with eigenvectors v1 = (3, 4) and v2 = (5,7), respectively. Find the matrix A and the powers A⁹⁹ and A¹⁰⁰.

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