2. Evaluate for the unknown variables Using the following, (a) Gauss-Jacobi Method (b) Gauss-Seidel Method and (c) Relaxation Method on given the system of linear equations. Terminate ifEa ≤ 0.0001 for all variables.127X24X1 - 3X3-15 = 6X1 - 3X3 - X211 = 10X3-X2 - 2X1

(a) Let X1=x, X2=y, X3=z By Gauss-Jacobi Method Total Equations are…

Answered: 2. Evaluate for the unknown variables…

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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3. Solve the linear system of equations x1 – *2 + 2x3 - -2, -201 +x2 – 03 – 2, 4x1 – x2 + 203 – 1, using 3 digit rounding arithmetic and Gaussian elimination with partial pivoting.
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?
Q1: Solve the linear system using Crammer rule: 2x + y + 2z = 4 x - 2y + 3z = 9 y - z = -3
2x + y + z = 10 Зх + 2у + 3z %3D 18 X + 4y + 9z = 16 [CLO1] The first step to solve the above linear system using Gaussian Elimination is to apply the following: row2 = row2 - m21 * row, Then, to apply the following: row3 = row2 – m31 * row, What are the values of m21 and m31? m21 = m31 =
The nonlinear system has six real solutions. 4x0 x₁ + x₂ = X0X3 xo - 2x₁ + 3x₂ = x₂x3 -xo + 3x₁ - 2x₂ = X₁ X3 x² + x² + x² = 1 (a) Show that if (x0, X₁, X2, X3)T is a solution, then (-X0, −X₁, −X₂, X3)¹ is also a solution.
4) Find the solution of the following linear equation system using LU decomposition method X1 + 2x2 + 3x3 = 5 2х1 — 4х2 + 6хз — 18 Зх1 — 9х2 — 3хз —D 6 -
Solve the system of linear equations by iteration method (4 iteration). x - 4 y +7 z = 10 5x - 4 y + z = 0 - 4x + 6 y - 4 z = 5 1. X= * X= 1/5(3y-2z) X= 1/5(3y-z) X= 1/5(4y-z) 2. y= * y= 1/6(5+4x-4z) y= 1/6(3y-z) y= 1/5(4y-z) 3. Z= * O z= 1/7(10-x-4y) Z= 1/6(3y-x) Z= 1/5(4y-4x) 4. When first iteration * O X= 0, Y=0.833, Z=1.905 X= 0, Y=1.833, Z=1.905 X= 0, Y=0.833 ,Z=3.905 5. When third iteration * X= 1.295 , Y=0.833, Z=3.241 X= 0, Y=1.833 ,Z=1.905 X= 1.295 , Y=3.495, Z=3.241 O O O O O O O O O
4.2) Solve the given system of equations using Gauss-Jordan Reduction method.
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Water is flowing through a network of pipes (in thousands of cubic meters per hour), as shown in the figure. (Assume F₁ - 700 and F₂-600. If the system has an infinite number of solutions, express X₁, X₂, X₂, X₁, X₁, X₁, and x, in terms of the parameterss and t.) R R 27 (b) Find the water flow when x₂-x₂ - 100. (X jo Xyo Xyp X qx Xxx X₂x Xy) = | 1/2 (a) Solve this system for the water flow represented by x₁, 1, 2,..., 7. (X ₂o Xyo Xyo Xxx Xxx X₂x Xy) = | (c) Find the water flow when x-x-Q. (X jo Xyo Xyo Xxx Xxx Xxx Xy). ·½/2 (d) Find the water flow when x-1000 and x₂ -0. (Жја Жул Жул
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2. Evaluate for the unknown variables Using the following, (a) Gauss-Jacobi Method (b) Gauss- Seidel Method and (c) Relaxation Method on given the system of linear equations. Terminate if Ea ≤ 0.0001 for all variables. 12 = 7X2-4X₁-3X3 -15 = 6X1 - 3X3 - X2 11 = 10X3-X₂ - 2X1