3. Solve the given systems of equations using the iterative method - Jacobi iterative orGauss-Seidel iterative methoda.b.3x - 5y = -8x + 2y = 12x+y -z = 13x + 4y + 2z = 13x - 5y-2z = 0

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Answered: 3. Solve the given systems of equations…

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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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?
2. Solve the linear system of equations (any method) for I1, 12, E3: I1 + 12 + I3 2x1 + 12 4x1 + 12 I3 2
Q1\ a- Solve the following system of equations by using Gauss elimination method x – 2y = -z 2x – 3z = 5 – y 4x – 7y +1 = -z
1) Solve the following system of equations by the Gauss-Jordan method. Write the solution if a unique solution exists. If no solution exists, write no solution. If infinitely many solutions exist, write infinitely many solutions, and express x, y, and z in terms of a parameter t. Show your work. x + y 10 z = -4 -x +7z = 5 (-3x - 5y +36z = 10) -
Solve the following system of four equations using Jacobi Method. Assume initial value of unknowns to be zero (0) with the ff % error of the variables: (x, = -2.49%, x2 = 1.98%, x3 = 3.78%, x4 = 4.18%). Use 4 decimal places for the entire computation. 3x2 – x3 + 8x4 = 15 10x1 – x2 + 2x3 = 6 X1 + 11x2 – x3 + 3x4 = 25 2x1 – x2 + 10x3 – x4 = -11
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
x+y+z=1 ×-y+5z=-9 2x+y+z=3 Use the Gauss- Jordan method to solve the system of equations.
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

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3. Solve the given systems of equations using the iterative method - Jacobi iterative or Gauss-Seidel iterative method a. b. 3x - 5y = -8 x + 2y = 1 2x+y -z = 1 3x + 4y + 2z = 13 x - 5y-2z = 0