Assume we have the following system of linear equation x1 + 4x2 = 5 x2 + 2x3 = 2 4x1 + 3x3 = 0 Note that a strictly diagonally dominant system guarantee the convergence of the methods such as Jacobi or Gauss-Seidal Method. After transforming the above system into a strictly diagonally dominant system and if we apply two steps of the Gauss-Seidal Methods from an initial guess (x1(1) , x2(1) , x3(1) ) = (0, 0, 0), then we get (x1(3) , x2(3) , x3(3) ). Fill in the following blanks by rounding in four decimal place. x1(3) = x2(3) =

Assume we have the following system of linear equation x1 + 4x2 = 5 x2 + 2x3 = 2 4x1 + 3x3 = 0 Note that a strictly diagonally dominant system guarantee the convergence of the methods such as Jacobi or Gauss-Seidal Method. After transforming the above system into a strictly diagonally dominant system and if we apply two steps of the Gauss-Seidal Methods from an initial guess (x1(1) , x2(1) , x3(1) ) = (0, 0, 0), then we get (x1(3) , x2(3) , x3(3) ). Fill in the following blanks by rounding in four decimal place. x1(3) = x2(3) =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 4CEXP

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