Assignment 2 - Solving Sets of Linear Equations - Due to December 25, 2011

1. Solve the following linear system by using Gauss-Jordan Method;
   $$\begin{array}{r} x_1+4x_2-3x_3+5x_4=45\\ -x_1-x_2+12x_3+x... ...x_2-8x_3+18x_4=151\\ 2x_1+11x_2+5x_3+17x_4=122\\ \end{array}$$
   1. Solve by hand.
   2. Solve by MATLAB.
      Hint: Modify the MATLAB codes (http://siber.cankaya.edu.tr/ozdogan/NumericalComputations/mfiles/chapter2/uptrbk.m uptrbk.m and/or http://siber.cankaya.edu.tr/ozdogan/NumericalComputations/mfiles/chapter2/GEPivShow.m GEPivShow.m)).
2. Solve the following linear system by using Gauss-Seidel Iteration;
   $$\begin{array}{r} 6x+y-3z=-7\\ 3x+5y+z=-4\\ 4x-y-2z=-2\\ \end{array}$$
   • Start by $P_0=(1,2,2)$.
   • Tabulate the iteration.
   • Compare with the Jacobi Iteration.
   Hint: Modify the MATLAB code for Jacobi Iteration (http://siber.cankaya.edu.tr/ozdogan/NumericalComputations/mfiles/chapter2/jacobi.m jacobi.m).