Question

# Consider the following system of linear equations: 2 \quad 2 x_{1}-6 x_{2}-x_{3}=-15 3-3 x_{1}-x_{2}+7 x_{3}=-35 -8 x_{1}+x_{2}-2 x_{3}=21 a) Solve the system of equations using matrix operations in Matlab (inv

and/or backslash \). b) Starting with initial guesses: x1 = x2, = x3, = 0, show two complete iterations using Gauss-Seidel iterative method. Evaluate the true and approximate errors of the second iteration. c) Redo part (2) using Jacobi Iterative methods. d) Redo part (2) using Gauss-Seidel with relaxation, with 2=0.8. e) Solve the system of linear equations by calling GaussSeidel dsolve or Isolvep, whicheverapplicable for the methods below. Report the number of iterations needed for achieving 6significant figures accuracy. i. Gauss-Seidel iterative method. 11.Jacobi iterative method. Print the iterations in a table format. iii. Gauss-Seidel with relaxation, with 1 = 0.8 and 2 = 1.25. iv. Compare the convergences in parts (a) to (c).

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