nswer the following using Jacobi Method. Show complete solutions. 1.) 15x + 2y - z = -200       2x + 12y + z = -250        x + 2y + 8z = 30

Algebra & Trigonometry with Analytic Geometry
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Chapter3: Functions And Graphs
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Answer the following using Jacobi Method. Show complete solutions.

1.) 15x + 2y - z = -200
      2x + 12y + z = -250
       x + 2y + 8z = 30

This is the example/ guide that might help.

 

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
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 |
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