Q.1 Solve the following system of equations using Cholesky decomposition method. 4x₁ + x₂ - X3 = 7, X₁ + 3x₂ - X3 = 8, -X1X₂ + 5x3 + 2x = -4, 2x3 + 4x₁ = 6.

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Q: Show that the order of the group of automorphism of a finite group of order n is a divisor of n!.

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