Question: [20 Marks] Consider the following linear system 3x + 2y4z - w = -9 7x-3y5z...

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Question: [20 Marks] Consider the following linear system 3x + 2y4z - w = -9 7x-3y5z + 2w = -6 x+y+z+w = 10 2xy + 5z - 3w = 3 a) Solve the system using Matlab/Octave rref, backslash, and the inverse commands. Call the solution X. Compute the spectral radius of the coefficient matrix. c) Use the 2-norm to Compute the condition number of the coefficient matrix. What the number tells you about the matrix. d) Use Matlab/Octave code to solve the system using the Jacobi method starting with initial value X (0) = (0.5,0.5,0.5,0.5, 0.5). Call the solution XJ. Print 10 iterations. [4] e) Use Matlab/Octave code to solve the system using the Gauss-Seidel method starting with initial value X (0) (0.5,0.5,0.5,0.5, 0.5). Call the solution XGS. Print 10 iterations. [4] f) Use Matlab/Octave code to compute the ||X- XJ||2 and ||X - XGS||for the errors in the approximation. [3] g) Are the two numerical methods converging to the solution? Which method is better to use. Justify your answer. [2] [3] [2] [2] Question: [20 Marks] Consider the following linear system 3x + 2y4z - w = -9 7x-3y5z + 2w = -6 x+y+z+w = 10 2xy + 5z - 3w = 3 a) Solve the system using Matlab/Octave rref, backslash, and the inverse commands. Call the solution X. Compute the spectral radius of the coefficient matrix. c) Use the 2-norm to Compute the condition number of the coefficient matrix. What the number tells you about the matrix. d) Use Matlab/Octave code to solve the system using the Jacobi method starting with initial value X (0) = (0.5,0.5,0.5,0.5, 0.5). Call the solution XJ. Print 10 iterations. [4] e) Use Matlab/Octave code to solve the system using the Gauss-Seidel method starting with initial value X (0) (0.5,0.5,0.5,0.5, 0.5). Call the solution XGS. Print 10 iterations. [4] f) Use Matlab/Octave code to compute the ||X- XJ||2 and ||X - XGS||for the errors in the approximation. [3] g) Are the two numerical methods converging to the solution? Which method is better to use. Justify your answer. [2] [3] [2] [2]

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This question presents a series of tasks related to a given linear system of equations Below Ill outline the steps one would follow to address each part of the question though I must note that I cant ... View the full answer