To ensure that the following system of equations, 2x, + 7x, - 11x, = %3D X+ 2x, + x, = -5 7x, + 5x, + 2x, = 17 converges using Gauss-Seidel Method, one can rewrite the above equations as follows %3D 2 7 -11 x, 6. (A) 1 2 1 X =-5

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 9OE
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To ensure that the following system of equations,
2.x, + 7x, - 11x, = 6
X + 2x, + x, = -5
%3D
7x, + 5x, + 2x, = 17
converges using Gauss-Seidel Method, one can rewrite the above equations as follows:
%3D
2 7 -11 x1
6.
(A)
1 2
1
X =-5
7 5
X3
17
7 5
2
17
(B)
1 2
1
r=-5
x2
27-11|| x3
6.
[7 5
(C)
1 2
1
X2
-5
27 -11 x,
17
(D) The equations cannot be rewritten in a form to ensure convergence
2.
2.
Transcribed Image Text:To ensure that the following system of equations, 2.x, + 7x, - 11x, = 6 X + 2x, + x, = -5 %3D 7x, + 5x, + 2x, = 17 converges using Gauss-Seidel Method, one can rewrite the above equations as follows: %3D 2 7 -11 x1 6. (A) 1 2 1 X =-5 7 5 X3 17 7 5 2 17 (B) 1 2 1 r=-5 x2 27-11|| x3 6. [7 5 (C) 1 2 1 X2 -5 27 -11 x, 17 (D) The equations cannot be rewritten in a form to ensure convergence 2. 2.
What is the approximate value of x in the
system
x + 3y + 52z = 173.61
x – 27y + 2z = 71.31
41x – 2y +3z 65.46
after three iterations of Gauss-Seidel
Method with initial estimates of
x = 1, y = -1, z = 3.
1.22999
1.32829
1.22856
1.23000
Transcribed Image Text:What is the approximate value of x in the system x + 3y + 52z = 173.61 x – 27y + 2z = 71.31 41x – 2y +3z 65.46 after three iterations of Gauss-Seidel Method with initial estimates of x = 1, y = -1, z = 3. 1.22999 1.32829 1.22856 1.23000
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