Let Q be an n x n orthogonal matrix. Let u € R" be an eigenvector of Q and define u² := {v € R¹¹\u • v = 0}. Show that if v is in u, then Qu is also in ut.

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Q: 1) Compute the order of a modulo 7 for a = 1,2,....6. Find all primitive roots modulo 7.

A: Order of the element

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Q: Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size…

A: Apply the improved Euler method to approximate the solution on the interval  with step size…

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Q: - Solve x²y” — 5xy′ + 8y = 4x² for the boundary conditions y(1) = 1, y′(1) = 1.

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