Solve the given system of linear equations using the Jacobi Method . The answer should have atleast 5 decimal places. Box thw final answer.1.) 3x1 - x2 + x3 = 2 2x1 - 3x2 - x3 = 7 3x1 - x2 + 4x3 = 5This is the example/ guide that might help. L3RD ITERATION:x₂ = 3-√₂+² 2 = 3-1 + 1.187533Yo = 7-2x₂-2₂- 2x2-2₂7-210-757-1-1875441.078125Z₂24-x₂+x2= 4 -(0-75) +1 1.06254។IterationYZO11.7510.7511-18751.06251.0781251.06250.9947921 0.953125 1.003906561.016927 1-001628 0-9895830-995985 | 0.994141 0.9961751.003030.9995391-000678As required, the difference of the last iterationShoulder be less than 0.005,| X=1; y = 1 ; 2=1234(1O5 decimalO= 1.0625 System of Linear Equations (Iterative Methods)Iterative methods are based on successiveimprovement of initial guesses for the solution.ITERATIVE METHODI: JACOBI METHODStep 1. Rewrite the systemStep 2. Initialize a value for the unknownsof zero.Step 3. Perform iteration until the values ofthe unknown don't diverge anymore.folutExample &肉丸 3x+2y2=34y+z=7X-y + 4z = 4Solution:NAAx = 3-y+z3Y= 7-2x-z4Z=4-x+x41st Iteration : x=0; y=0,2 = 0X, = 3-ото= 1Y₁ = 7-2(0) - (0)= 1.752,4-04 으= 142ND ITERATION:x₂ = 3-y₁ +2₁= 3 ~ 1.75 +1 = 0.7533Y2:7-2x, 7,7-20)-(144Z₂ = 4-X₁tY₁ = 4-1+1.7544= 1.1875

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3RD ITERATION: x₂ = 3-X₂ +2₂ 3-1 + 1.1875 = 1.0625 3 3 Yo= 7-2x₂₁-22-7-2 10.757-1-1875 4 4 1.078125 F 23 = 4-X₂+x₂ - 4 - (0-75) +1 H = 1.0625 4 9 Iteration Y O 1 2 O Z 5 decimal O O 1 1.75 1 0.75 1 1-1875 3 1.0625 1-078125 1.0625 4 0.994792 0.953125) 1-003906 S 1.016927 1.001628 0-989583 6 0-995985 0.994141 0.996175 0.999539 1-000678 1.00303 As required, the difference of the last iteration Should be less than 0.005, X=1; y = 1 ; 2=

3RD ITERATION: x₂ = 3-X₂ +2₂ 3-1 + 1.1875 = 1.0625 3 3 Yo= 7-2x₂₁-22-7-2 10.757-1-1875 4 4 1.078125 F 23 = 4-X₂+x₂ - 4 - (0-75) +1 H = 1.0625 4 9 Iteration Y O 1 2 O Z 5 decimal O O 1 1.75 1 0.75 1 1-1875 3 1.0625 1-078125 1.0625 4 0.994792 0.953125) 1-003906 S 1.016927 1.001628 0-989583 6 0-995985 0.994141 0.996175 0.999539 1-000678 1.00303 As required, the difference of the last iteration Should be less than 0.005, X=1; y = 1 ; 2=

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.FOM: Focus On Modeling: Making The Best Decisions

Problem 6P

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