Denote by the set of all n X nwhere thelinear systems Aπ = 6,coefficient matrix A is strictlydiagonally dominant.Then, for each of the elements of X,the Jacobi method, applied with a verygood initial approximation to thesolution of the system, will generatea sequence of approximations that willnot converge to the true solution ofthe system.O TrueO False

Answered: Denote by the set of all n X n linear…

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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Solve the following system using the Gaussian algorithm: 2x1 – x2 + 3x3 = 1 -2x1 + x2 – X3 = 2 X1 — Зх2 + 6х3 = 3 X1 Let x be the vector x = x,, where x1, x2 and x3 are solutions of the system, and y be the vector y = 1|. Evaluate the (X3) scalar product of x and y. [Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer. So for example, if the correct answer is 6.78 then any input that lies between between 6.53 and 7.03 will be marked as correct.]
Let k be a real number. By using Cramer's rule, the solution of the following system is: (2x + 2y = 2k | 2x + 3y = 0 O x-3k, y=6k O x=7k, y=4k None of these x-3k, y=-2k Which of the following sets is linearly independent?" M-{ (1,2),(2,4), (-1,-2)}
Find the solution using the Jacobi method and Gauss-Seidel method for the following linear systems, using x(0) = 0: 2x1 - x2 + x3 = -1, 2x1 + 2x2 + 2x3 4, -X1 - X2 + 2x3 = -5 and justify that which metod is fast.
Consider the following linear system: 1 2 X1 3 (6) X2 Assume that, due to numerical error, the linear system (6) is solved with the same matrix, but with a slightly different right hand side: 1 2 X1 3.01 (7) 3 4 X2 7.02 Without calculating the solutions of the linear systems (6) and (7), mate the relative error in the 1-norm, | : 1. esti-
Solve the following system using the Gaussian algorithm: 2x1 - x2 + 3x3 = 0 -2x1 + x2 - X3 = -2 x1 - 3x2 + 6x3 = 3 Let x be the vector x = |x2, where x1, x2 and x3 are solutions of the system, and y be the vector y =|1 Evaluate the scalar product of x and y. [Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer. So for example, if the correct answer is 6.78 then any input that lies between between 6.53 and 7.03 will be marked as correct.] Answer:
Solve the following system using the Gaussian algorithm: 2x1 - x2 + 3x3 = 3 -2x1 + x2 – x3 = 0 x1 - 3x2 + 6x3 = 3 Let x be the vector x = x2l, where x1, x2 and x3 are solutions of the system, and y be the vector y = 1. Evaluate the scalar product of x and y. 0.
5. Find the basis for and the dimension of the solution space of the homogeneous system of equations. 2x1+4x2+3x3-6x4=0 X1+2x2+2x3-5x4=0 3x1+6x2+5x3-11x4-0
The augmented matrix [A|b] of an inhomogeneous linear system is row equiv- alent to the matrix (1 0 -2 0 0 1 0 0 0 0 3 4. -6 | 9 0 0 | 1. 8. Express the solution set to L in the form p+ Span(B) where p is a particular solution to the system L and Span(B) = null(A).
Determine the set of all basic solutions and basic feasible solutions of the following poly- hedron: P = {x € R4 : 3x1 – 4x2 + 2x3 – x4 = 1; –2x1 + 2x2 – x3 + x4 = 1; x > 0}. For each basic solution and basic feasible solution, determine whether it is degenerate or nondegenerate. You can assume that the coefficient matrix A has full row rank.
Find the sum of components (x, (2) +x₂ (2) +x, (2) of second iteration of the Jacobi method for the following linear system, using the initial iteraion x(0)=0 X₁-X₂-6X3=3, X₁-2x₂+4x₂=3, 3x1-x₂-3x3=4. O-2 O -7 05 O4
take k as 1
Solve the following system using the Gaussian algorithm: 2x1 – x2 + 3x3 = 0 -2x1 + x2 – X3 = -1 X1 — Зx2 + 6хз = 3 X1 Let x be the vector x = |x2, where x1, x2 and x3 are solutions of the system, and y be the vector y 1|. Evaluate the scalar product of x X3, and y.

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