In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x, X2, . . . , x„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. Зх, x2 = 2 2. – 4x, + 2x, = -6 %3D x, + 4x, = 5 1 %3D 3. 2х, = 2 4. 4x, + x, + x3 = 7 x, - 7x, + 2x; = -2 + 4x3 - х, X, - 3x, + x3 = -2 -X, + x2 - 3x3 = -6 %3D 3x1 11 %3D
In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x, X2, . . . , x„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. Зх, x2 = 2 2. – 4x, + 2x, = -6 %3D x, + 4x, = 5 1 %3D 3. 2х, = 2 4. 4x, + x, + x3 = 7 x, - 7x, + 2x; = -2 + 4x3 - х, X, - 3x, + x3 = -2 -X, + x2 - 3x3 = -6 %3D 3x1 11 %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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Please answer number 3
![8:39 O V A •
Bllll 68%i
In Exercises 1– 4, apply the Jacobi method to the given system of
linear equations, using the initial approximation (x, X2, . . . , X„) =
(0, 0, . . . , 0). Continue performing iterations until two successive
approximations are identical when rounded to three significant digits.
1. Зх, — х, %3D 2
2. - 4x, + 2x, = -6
x, + 4x, = 5
Зх, — 5х, —
1
3. 2х, — х,
4. 4x, + x, + x3 =
7
=
x1 - 3x, + xz = -2
-x, + x, - 3x = -6
x - 7x, + 2x; = -2
3x,
+ 4x3 = 11
5. Apply the Gauss-Seidel method to Exercise 1.
6. Apply the Gauss-Seidel method to Exercise 2.
7. Apply the Gauss-Seidel method to Exercise 3.
8. Apply the Gauss-Seidel method to Exercise 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6a08047-2e29-4756-ae04-96331026d654%2F6cd5e7de-eb85-4607-8c01-f5236ef2f4bf%2Fphw1ki8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8:39 O V A •
Bllll 68%i
In Exercises 1– 4, apply the Jacobi method to the given system of
linear equations, using the initial approximation (x, X2, . . . , X„) =
(0, 0, . . . , 0). Continue performing iterations until two successive
approximations are identical when rounded to three significant digits.
1. Зх, — х, %3D 2
2. - 4x, + 2x, = -6
x, + 4x, = 5
Зх, — 5х, —
1
3. 2х, — х,
4. 4x, + x, + x3 =
7
=
x1 - 3x, + xz = -2
-x, + x, - 3x = -6
x - 7x, + 2x; = -2
3x,
+ 4x3 = 11
5. Apply the Gauss-Seidel method to Exercise 1.
6. Apply the Gauss-Seidel method to Exercise 2.
7. Apply the Gauss-Seidel method to Exercise 3.
8. Apply the Gauss-Seidel method to Exercise 4.
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