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Solve the system of linear equations Зх, — х, %3D2 X, +4x, = 5 using Jacobi iterative method with an initial approximation, x° = (0,0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits.

Solve the system of linear equations Зх, — х, %3D2 X, +4x, = 5 using Jacobi iterative method with an initial approximation, x° = (0,0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits.

Advanced Engineering Mathematics
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 system of linear equations 3x, – x, = 2 X +4x, = 5 using Jacobi iterative method with an initial approximation, x° = (0,0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits.
Transcribed Image Text:Solve the system of linear equations 3x, – x, = 2 X +4x, = 5 using Jacobi iterative method with an initial approximation, x° = (0,0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits.
Expert Solution
Step 1

We have to use the Gauss Jacobi iterative method to perform iterations for the

following linear system of equations:

3x1-x2=2x1+4x2=5

Let the initial approximation is denoted as x10, x20=0, 0. Rearranging the

equations we get,

x1=13x2+2x2=14-x1+5

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