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Q1) In this question, you will use the Gauss-Seidel method to solve systems of linear equations. The Python code for the Gauss-Seidel iterations is provided to you at the end of this question. Some information about the Python code: a) Recall that Xx is the vector generated by the Gauss-Seidel iterations. b) The Python code performs 20 iterations of the Gauss-Seidel method. After 20 iterations, the code prints the value of xx. C) The Python code has the vector d. The kth component of vector "d" is the largest element of X: Xx-1). That is, dk = max max Xx - XX-11. d) The Python code has the vector "Itr that contains the index of iterations. e) You need to enter the entries of matrix A and vector of the Gauss-Seidel method into the Python code. The Python code will not find the right answer if you entry the entries of A and b (instead of A and b). f) You need to enter the entries of initial vector X, into the Python code. 1. Consider the following system of linear equations. Find the matrix A and the vector 5 which are used in the Gauss-Seidel iterations. Include the steps in your report. (3 marks) 5 3 1 4 1 x (1) 1 1 3 3 2. Check if matrix A in the system of linear equations above is diagonally dominant? Include the steps in your report. (3 mark) 3. Enter A and B (from Part 1) and Xo = [2,2, 2] into the Python code. Run the code to solve the system of linear equations. Include the output of the code in your report. (1 mark) 4. Plot the vector d versus "Itr. Include the plot in your report. (1 mark) 5. In your plot from Part 4, what will happen as the number of iterations increases? (2 marks) 6. Consider the following system of linear equations. Find the matrix A and the vector 5 which are used in the Gauss-Seidel iterations. Include the steps answer in your report. (3 marks) 5 10 4 1 4 1 = (2) 1 1 3 6 7. Check if matrix A of the system of linear equations in (2) is diagonally dominant? Include the steps in your report. (3 mark) 8. Run the code with A and B from Part 6 and Xo = [2, 2, 2]. Include the output of the code in your report. (1 mark) 9. Plot the vector d versus Itr for Part 8. Include the plot in your report. (1 mark) 10. Does the Gauss-Seidel method find the solution of system of linear equations in (2)? If not, why? (2 marks) Hint: Check if the output of the code in Step 8 satisfies (2). Hint: Check if the matrix A in (2) is diagonally dominant. Python code of the Gauss-Seidel method: import numpy as np import matplotlib.pyplot as plt import math At np.array matrix A [[0,0,0], [0,0,0], [0,0,0]]) bt= np.array( [[O], [0].[0]]) vector 6 X0= np.array( [[0].[0].[0]]) Iteration=20 S=C3.Iteration) Initial vector x X = np.array(np.zeros(s)) d= np.zeros(Iteration) X[:30]= np.transpose(bt-np.matmul(At.XO)) d[0]= np.amax(np.abs(np.reshape(X[30].3.1))-X0)) for i in range(1,Iteration): X[:1)= np.transposebt-np.matmul(At, np.reshape(X[:1-1],3,1)))) Maximum of the d[i]= np.amax(np.abs(X[...]-X[:1-1])) difference vector print("The solution is", X[:1]) Itr= np.linspace(1, Iteration. Iteration) Number of iterations