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(30 points) The linear system Ax -b with has the unique solution x = [1 1]T. (a) (10 points) Determine by hand the RJ-D (L
(30 points) The linear system Ax -b with has the unique solution x = [1 1]T. (a) (10 points) Determine by hand the RJ-D (L + U) and Rcs(L D)-U, that is, the Jacobi and Gauss-Seidel iteration matrices, respectively (of course you may use MATLAB to verify your answers) (b) (5 points) Find the oo-norm and spectral radius of R, and RGs (c) (15 points) Perform 5 iterations of both Jacobi and Gauss-Seidel methods using Xo-[00]?. For each present your results in a table with the following format . column 1: k (iteration step) . column 2: ?(k) (1st component of the computed solution vector at step k) column 3: (2nd component of the computed solution vector at step k) column 4 lrror norm at step k) column 5:lle& (ratio of successive error norms at step k) Which method is converging faster? Justify your
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