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

Answered: Image /qna-images/answer/f157e07c-d388-4d24-9943-7d1b1b1d279e.jpg

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=

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: A. Graph the system of linear equations. 4x − 5y = 11 2x + y = 9 B. Solve the system. (If…

A: A system of equation is a collection of two or more equation with common set of unknowns. The…

Q: 1. Solve the system of linear equation. x+ y+ 3z = 2 3x – 2y + 2z = -2 3x + 2y + 8z = 6

A: As per bartleby guidelines, for more than one question, only 1st one is to be answered. Please…

Q: 1.2 Solve the following system of equation using Crammer's rule: 3x – 2y+: = 6 2x+3: =3 4x - y+5: =…

Q: 11) y = −4x + 8 4 2 1 -4x + 8 y -4(4) 48-8 (-4(2) +8 -4015+8/4 -86 4 -2 8 6 2 10 121 4 -2 -4 -6 (x,…

Q: Use Cramer's rule to compute the solutions of the system. 2x₁ +7x₂=8 6x₁ + 3x₂ = -12 What is the…

Q: DIRECTION/S: Choose the correct answer on your answer sheet. 1. A set of two or more linear…

Q: -4x1 + 2x2 + 3x3 = -8 %3D 2x1 – 2x2 – 4x3 = 0 | -3x1 – 4x2 + 5x3 = 5 |

A: To solve the set of equations using the Cramer's rule, the first step is to write all these…

Q: 1. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y =…

Q: 2x1 -3x1 6X2 — X3 X3 = -38 1x₂ + 7x3 -34 - - 2x3 = -20 -8x1 + X2 =

Q: 4. Using elimination, solve the system 3 3x+4y =1 2x + 3y = 3 Give the pivot and multiplier.

Q: quadratic linear constant equation, also called a(n) ▼ second third first -degree equation.…

A: ax2+bx+c = 0where , a,b,c are real numbersand a≠0

Q: Activity 3: Situation: Nowadays, mobile phone is very essential in every person's life. You can send…

Q: The system of linear equations: a1 + a2 + a3 2x1 - 22 - a3 = 6 = 3 is: Select one: O a. a 2 x 3…

A: A system of equations with m equations and n variables is said to be a m×n system. A system is…

Q: Amerchant buys 3 types of goods. The price of typeXis $50, typeY is $75 andtypeZ is $20. The…

Q: 9. Solve the system of equations any way you wish. Show all your work. (x+2)²+(y-2)²%D1 y = -(x+2)²…

Q: y = C¡e e-2= + Cze³* + C2e%

Q: Q1: solve the system of linear algebraic equations using Cramer's Rule. 6X-3Y+ 12Z = 15 2X +3Y+5Z =…

A: The given system of equations is: 6X-3Y+12Z=152X+3Y+5Z=104X-2Y+8Z=21 Solve the given system of…

Q: If the ratio of boys to girls in tennis camp is 3:5 if there are 64 campers, how many are girls

A: We find out how many girls as follows: • We first need to determine the total number of parts in…

Q: Consider the system of equations Find all basic solutions. x1 01 x2 -1 2 x3 x4 [21 1 12 = 2

Q: 7 1*11 X2 --2 -4 7 8. |-9 |-4 10 -6 12 9 -12||X3 -11] Lx4 9. -5 8 -12 -8 -3. ||

Q: Help use elimination to find all solutions of the system in image attached

Q: Place the correct system of equation with the correct soultion: 1. y = x+5, y=x 2. y =…

A: Solve the (1) system of Equations,

Q: 1 of 8 Automatic Zoom 2. MiKayla has $30 in a cafeteria account. She spends $3 each day for lunch.…

Q: Hi, can I please have this practice question answered? Thank you!

Q: Use Cramer's rule to solve the given system. 6x - y = 8 Зх + Зу %3D6 The solution set is { }.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want to…

Q: Hhe following system Solue 3. 2x,-30cz -6x3-5xy +2xs=7 C3+ 3>c4 -7>c5=6 xy-2>c5=1

A: The system is 2x1-3x2-6x3-5x4+2x5=7x3+3x4-7x5=6x4-2x5=1 From the last equation x4=1+2x5

Q: An amusement park has two new rollercoasters. The number of people in line to ride each…

A: according to question, an amusement park has two new rollercoasters. the number of people in line to…

Question

100%

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 = 5

This is the example/ guide that might help.

L
3RD ITERATION:
x₂ = 3-√₂+² 2 = 3-1 + 1.1875
3
3
Yo = 7-2x₂-2₂
- 2x2-2₂
7-210-757-1-1875
4
4
1.078125
Z₂
2
4-x₂+x2= 4 -(0-75) +1 1.0625
4
។
Iteration
Y
Z
O
1
1.75
1
0.75
1
1-1875
1.0625
1.078125
1.0625
0.9947921 0.953125 1.003906
5
6
1.016927 1-001628 0-989583
0-995985 | 0.994141 0.996175
1.00303
0.999539
1-000678
As required, the difference of the last iteration
Shoulder be less than 0.005,
| X=1; y = 1 ; 2=1
2
3
4
(1
O
5 decimal
O
= 1.0625

System of Linear Equations (Iterative Methods)
Iterative methods are based on successive
improvement of initial guesses for the solution.
ITERATIVE METHODI: JACOBI METHOD
Step 1. Rewrite the system
Step 2. Initialize a value for the unknowns
of zero.
Step 3. Perform iteration until the values of
the unknown don't diverge anymore.
folut
Example &
肉丸 3x+2y2=3
4y+z=7
X-y + 4z = 4
Solution:
NAA
x = 3-y+z
3
Y
= 7-2x-z
4
Z=
4-x+x
4
1st Iteration : x=0; y=0,2 = 0
X, = 3-ото
= 1
Y₁ = 7-2(0) - (0)
= 1.75
2,4-04 으
= 1
4
2ND ITERATION:
x₂ = 3-y₁ +2₁= 3 ~ 1.75 +1 = 0.75
3
3
Y2:7-2x, 7,7-20)-(1
4
4
Z₂ = 4-X₁tY₁ = 4-1+1.75
4
4
= 1.1875

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

solve the system of linear equations using LU factorization method X₁ + 2X₂ + 3X3 + 4X4 = 7 2X₁ +5X₂ + 8X3+ 11X4 = 16 3X₁ + 8X₂ + 14X3 + 20X4 = 32 4X₁ + 11X₂ + 20X3 + 30X4 = 48
Equal Fractions
Direction: Graph the given system of linear equations using the Intercept- Method. 3x + 2y = 6 ix+ 2y = 4 y 2x-1 2. ly = x+2 1.
Solve the system of equations by either the addition method or the subtitution method. Express numbers as integers or decimals. -0.1x+0.1y=0.2 0.1x+0.1y=0.1 The solution set is( , )
None
Hello. Please answer the attached Linear Algebra question correctly and completely. Please show all of your work. *If you answer the question correctly and show all of your work, I will give you a thumbs up. Thanks.