4. Estimate the solution to the following system of linear equations using two iterations of Gauss-Seidel Iterative Method when the initial values of y,, y2, and y; are 5, 10, and 0, respectively:-8y, + y2- 2y3 = -202y1- 6y2- y3 = -38-3y,- y2 + 7y3 = -34

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Answered: 4. Estimate the solution to the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Determine the solution of the system of equations [a][x]=[b] using the Gaus elimination method, where -2 [X1 10 2 and b -5|,x = |X2 [X3] a = -16 -1 8.
Obtain the solution set of the linear equation system given below by using the Jacobi method.Take the initial values 0.NOTE: Proceed only 7 iterations.
1. Of the following three sets of linear equations, identify the set(s) that you could not solve using an iterative method such as Gauss-Seidel. Set One Set Two Set Three 8x + 3y + z = 12 -6x + 7z = 1 2x + 4y - z = 5 x + y + 5z = 7 x + 4y - z = 4 3x + y - z = 4 -x + 3y + 5z = 7 -2x + 4y - 5z = -3 2y – z = 1 %3D MIND
1. (a) Use definition of linear transformation to determine whether the transformation T:R? → R³ defined as follows is linear. -y T r+ 2y 2.r – 4y (b) Let T : R" → R" be a linear transformation. i. Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify. ii. Does S(0) = 0 mean that S is linear? If not, can you give a counter-example? (c) Consider the following matrix transformation T : R² → R² defined as a b T d i. If T rotates the 2D space 150° counter-clockwise, and then reflects the result across the new r-axis, find a, b, c, d. ii. What if T reflects the 2D space across the r-axis first and then rotates 150° counter-clockwise? Do you expect to get the same a, b, c, d? Why or why not?
Given the linear system 2х, — бх, — х, — -38 -3x, – x, +7x, =-34 -8x, +x, – 2x, =-20 determine the values of X1 , X2 and X3 using 1. Jacobi Iterative Method; 2. Gauss-Seidel Iterative Method. Note: Do iterations until the approximate error is less than 5%.
Solve the following linear system of equation using the Gauss-Jordan Elimination method
3. Solve the system of linear equations, using the Gauss-Jordan elimination method. Show all steps and indicate all row operations using correct notation as shown in the lecture. State the general solution using the parameter t. Then give two particular solutions, one where t = -1 and one where t = 1. X-Z=-2 2x-y=0 3x-y-z=-2
Q1) Solve the following system of linear independent equations using Gauss-Jordan Elimination method, 2x – 4y + 5z = 36 -3x + 5y + 7z = 7 5х + Зу—8z %3D —31

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4. Estimate the solution to the following system of linear equations using two iterations of Gauss- Seidel Iterative Method when the initial values of y, y2, and ys are 5, 10, and 0, respectively: -8y, + y2- 2y3 = -20 2y1- 6y2- y3 = -38 -3y,- y2 + 7y3 = -34