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I need 7.1 (matlab) Crank-Nicolson. Observe that small time steps were taken initially because of the large derivatives in the solution, and that much larger

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I need 7.1 (matlab)

Crank-Nicolson. Observe that small time steps were taken initially because of the large derivatives in the solution, and that much larger steps became possible once the solution smoothed out. 90 Chapter 7. Scientific Computing Exercises 7.1. Write a function or script that solves the linear system Ah = b for a square matrix A and positive integer k, using an LU factorization of A and never explicitly computing the matrix A. (Hint: Interpret the problem as solving k linear systems sequentially.) 7.2. Suppose A is a full-rank 6 4 matrix, which of the following is (in exact arithmetic) equal to an identity matrix: A\A or A/A? Why is the other case something other than the identity

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