1) Consider the following system.4x1 + x2 – x3 + x4-2xi + 4x2 – 3 – x4-1-x1 – x2 + 5x3 + x4x1 – x2 + x3+3x41(0)a) Find x(2) using the Jacobi method with x(0)= 0 and x" = 0.b) Find Jacobi matrix for this problem.(0)

Solving system of linear equations by Jacobi method Let x1=x,x2=y,x3=z,x4=w x(2) means upto second…

Answered: 1) Consider the following system. 4x1 +…

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. (a) Find the condition number of the coefficient matrix in the system X1 (1461) (²2) = (2²6) X2 as a function of d > 0. (b) Find the error magnification factor for the approximate root xa = (-1,3+6).
1. (a) Is there any 4 x 7 matrix A that satisfies Nullity(A) = 2. If yes, find an example of such A; if not, explain your answer. (b) Is there any 10 x 5 matrix B that satisfies Rank(B) = 7. If yes, find an example of such B; if not, explain your answer. (c) Is there any 5 x 6 matrix C that satisfies Nullity(C) = 2. If yes, find an example of such C; if not, explain your answer.
A linear systje is defined by the following equatiosn, -x1 + x2 – x3 -1, 2.x1 + 6x2 – x3 6x1 + 5x2 + 3x3 3, 8. %3D From this linear system answer the following: (a) soning. Does the system have unique solution or infinite solution? Explain or show calculation with rea- (b) Find the augmented matrix for the linear system. (c) Solve the system using Gaussian elimination method.
Please solve this question in handwriting. Again please need it in handwriting.
[3x 6х —2х] -x 5) The matrix A = , then multiplication of A * A = A? is : a) 6x 2x2! 3x2 -x2] b) x² % 9. с) х [36 d) x\i/6 [1/3 1/1] 1/2]
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(a) A is a 3 x 3 matrix and 2(A + I) = I. Enter det (A + I). (b) A is a 2 x 2 matrix and 2 A + 5 I = 0. Enter det (4+ I). (c) A is a 4 x 4 matrix and 42 - 4 A -21 1= 0. If det (A-21) > 0, enter det (4-21).
U and = span{[-3 4 5],[-11 -2 3]} W = span{[ span{[−4 x = [ UnW = −1 5],[-12 -1 1x×3 of V = R¹×³. Find a matrix X € V such that E 5], [-12 -5 9]} = span{X}.
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:
8. Solve the linear system Ax-b by x₁ + x₂-3x₂ = -1 -x₁ + 2x₂ = 1 x₁ - x₂ + x₂ = 2 a) finding the LU-factorization of the coefficient matrix A b) Solving the lower triangular system Ly-b. c) solving the upper triangular system Ux-y.
1) (i) Given any m x n matrix, A, show that A· A¹ and A¹. A must both be defined and T (ii) both must be square matrices. (iii) Show that (A.A¹) = A.A¹ for any matrix A. (Prove these results in general. Do not just give an example.)
8 5 0 For the matrix A = 2 5 4 4 4 9/ cofactor C23?

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1) Consider the following system. 4x1 + x2x3 + x4 x₁ + 4x2x3 x4 -x1 - x2 + 5x3 + x4 X1 X2 + x3 + 3x4 a) Find (2) using the Jacobi method with (0) (0) x₂ = 0 and x) = 0. x2 b) Find Jacobi matrix for this problem. || = (0) ₁ -2 -1 0 1 = 0,