This problem needs to be done on MATLAB, basic 2021 program no python etc. For this problem, I am given a System of Linear Equations (Equation 1) and for part A it needs to be solved with two different methods (Jacobi and Gauss-Seidel Iterative methods, a picture states this and what needs to be done (initial guesses given, how many iterations need to be done, and making a plot RTE with use of log 10 vs number of iterations). And then the second part of the question requires using the result from part a and computing a condition number, C, and then still using the Gauss-Seidel Method, plotting it with 3 curves all in the same plot and they are given in the picture as well where it says part b. But what I need from you is the codes to perform these tasks as well as the outputs and what happens when the code runs (screenshots of the codes and seeing the outputs, this being plots and answers, etc). Make sure to read all the second pictures where it explains exactly what needs to be done, as the first picture shows the linear equations system and then just gives background and other equations to help.

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A system of linear equations is given: 7 4 2 0.5 3 1 X2 (+590-0 2 X3 2 0.5 4/ \X4 Symbolically, we write Eq. (1) as Ax=b, Eq. (2) which also gives the definitions of the matrix A and vectors and b. For this system, the exact solution is known to be 1.5 1 XS = RTE = 3 NW RRS = 2 |le|| ||||' 23.5 12 Let us also recall a few relevant definitions. Given X as a numerical solution, the relative true error (RTE) is defined as " 15 12 Eq. (3) where è = x - xs is the vector of absolute error. The relative residual (RRS) is defined as |||| ||b|| Eq. (1) Eq. (4) where r = AXN - b is the residual vector. The key conclusion of the discussion (in Lecture 11) on condition number, C, is summarized by the inequality, * (RRS) ≤ (RTE) ≤ C* (RRS). Eq. (5) Conceptually, Eq. (5) provides the upper and lower bounds of RTE from RRS and C. The condition number itself is defined by C = ||A||||A¹|| . Eq. (6) In Eqs. (3)-(6), Euclidean norm is used for a vector and Euclidean 2-norm (or "Frobenius norm") is A system of linear equations is given: 7 4 2 0.5 3 1 X2 (+590-0 2 X3 2 0.5 4/ \X4 Symbolically, we write Eq. (1) as Ax=b, Eq. (2) which also gives the definitions of the matrix A and vectors and b. For this system, the exact solution is known to be 1.5 1 XS = RTE = 3 NW RRS = 2 |le|| ||||' 23.5 12 Let us also recall a few relevant definitions. Given X as a numerical solution, the relative true error (RTE) is defined as " 15 12 Eq. (3) where è = x - xs is the vector of absolute error. The relative residual (RRS) is defined as |||| ||b|| Eq. (1) Eq. (4) where r = AXN - b is the residual vector. The key conclusion of the discussion (in Lecture 11) on condition number, C, is summarized by the inequality, * (RRS) ≤ (RTE) ≤ C* (RRS). Eq. (5) Conceptually, Eq. (5) provides the upper and lower bounds of RTE from RRS and C. The condition number itself is defined by C = ||A||||A¹|| . Eq. (6) In Eqs. (3)-(6), Euclidean norm is used for a vector and Euclidean 2-norm (or "Frobenius norm") is

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