Answer the following using Jacobi Method. Show complete solutions. The answer should have atleast 5 decimal places in order to getless than .005 differemce in last iteration. 2.) 9x1 - 13x2 + 4x3 = 111      4x1 + 22x2 -13x3 = -128      8x1 + 8x2 + 17x3 = 10 This is the example that might help

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 30HP
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Answer the following using Jacobi Method. Show complete solutions. The answer should have atleast 5 decimal places in order to getless than .005 differemce in last iteration.
2.) 9x1 - 13x2 + 4x3 = 111
     4x1 + 22x2 -13x3 = -128
     8x1 + 8x2 + 17x3 = 10

This is the example that might help.

 

 

Sheuld oo be less than 0.005,
5 decimdl
3RD ITERATION:
メッ=3- y2t2,
%3D
3-1+1.1875
=1.0625
%3D
Yo:フ-2x, -Z2
7-210.75)-1-1875
こ
1.078125
2,- 4-メetyz 4 - C0-75) +|
%3D
i,0625
4
'Iteration
1
1.75
2.
0-75
|-1875
3
1.0425
1.078125
U -994792 0.953125 1.003906
10625
4
1.016927
1-001628 0-989583
0-995985 0.994141 0.990175
0.09953
7
1-000676
1.00303
As required, the difference of the last iteaticn
1に2、1:んり1こメ
|
Transcribed Image Text:Sheuld oo be less than 0.005, 5 decimdl 3RD ITERATION: メッ=3- y2t2, %3D 3-1+1.1875 =1.0625 %3D Yo:フ-2x, -Z2 7-210.75)-1-1875 こ 1.078125 2,- 4-メetyz 4 - C0-75) +| %3D i,0625 4 'Iteration 1 1.75 2. 0-75 |-1875 3 1.0425 1.078125 U -994792 0.953125 1.003906 10625 4 1.016927 1-001628 0-989583 0-995985 0.994141 0.990175 0.09953 7 1-000676 1.00303 As required, the difference of the last iteaticn 1に2、1:んり1こメ |
Step 3. Perform iterction until the values af
System of Linear Equations (Iterative Methads)
Iterative methads ave based on successive
improvement of initial quesser for the sdlution
ITERATIVE METHUDI : JACORI METHOD
Step 1. Rewrite the system
Step 2. Initialize
a value for the unknouns
of zeru.
tep 3. Perform iterction until the values al
the unknawn dan't divevge anymore.
falut
Example:
A 3xty-Z =3
2×+4y+zニフ
Solution:
そtん-e = メ
Y=7-2x-Z
4
Z:4-xty
スキメーh
: x:0; y=0,2=0
Ist Itercition
X,こ3-0+O
3
Y.= 7-2(0) - (0?
=1.75
Z,?4-04 O
4
2ND ITERAION:
メ2ラーy,ナ21-3-175+l>0.75
3
3
Y2:1-2x,*2フー2-D.1
そz: 4-Xty、 4-1t15
4-1+1.75
=1.1875
Transcribed Image Text:Step 3. Perform iterction until the values af System of Linear Equations (Iterative Methads) Iterative methads ave based on successive improvement of initial quesser for the sdlution ITERATIVE METHUDI : JACORI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknouns of zeru. tep 3. Perform iterction until the values al the unknawn dan't divevge anymore. falut Example: A 3xty-Z =3 2×+4y+zニフ Solution: そtん-e = メ Y=7-2x-Z 4 Z:4-xty スキメーh : x:0; y=0,2=0 Ist Itercition X,こ3-0+O 3 Y.= 7-2(0) - (0? =1.75 Z,?4-04 O 4 2ND ITERAION: メ2ラーy,ナ21-3-175+l>0.75 3 3 Y2:1-2x,*2フー2-D.1 そz: 4-Xty、 4-1t15 4-1+1.75 =1.1875
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