For each one of the following systems of linear equations: I) 20 8x1 + 3x2 12.x2 + 6x3 X1 + 10r3 30 10 II) 2x1 + a2 + 5a3 2.x1 + 2a2 + 2x3 = 1 4.r1 + a2 = 2 1 III) x1 + x2 - a3 = -3 6x1 + 2a2 + 2x3 = 2 -3.x1 + 4x2 + x3 = 1 (a) Use Gaussian Elimination to compute the determinants required to solve the system using Cramer's Rule. (b) Use Gaussian Elimination to compute the inverse of A. (c) Use the inverse to solve the system of equations. (d) Use Jacobi's Method to solve the system of equations. Start with a vector of l's as initial approximation, e = 10-4. It is recommended that you use Excel or write a program in Java to help you. (e) Use Gauss-Seidel's Method to solve the system of equations. Start with a vector of l's as initial approximation, e = 10-4. It is rec- ommended that you use Excel or write a program in Java to help you.
For each one of the following systems of linear equations: I) 20 8x1 + 3x2 12.x2 + 6x3 X1 + 10r3 30 10 II) 2x1 + a2 + 5a3 2.x1 + 2a2 + 2x3 = 1 4.r1 + a2 = 2 1 III) x1 + x2 - a3 = -3 6x1 + 2a2 + 2x3 = 2 -3.x1 + 4x2 + x3 = 1 (a) Use Gaussian Elimination to compute the determinants required to solve the system using Cramer's Rule. (b) Use Gaussian Elimination to compute the inverse of A. (c) Use the inverse to solve the system of equations. (d) Use Jacobi's Method to solve the system of equations. Start with a vector of l's as initial approximation, e = 10-4. It is recommended that you use Excel or write a program in Java to help you. (e) Use Gauss-Seidel's Method to solve the system of equations. Start with a vector of l's as initial approximation, e = 10-4. It is rec- ommended that you use Excel or write a program in Java to help you.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. For each one of the following systems of linear equations:
I)
8x1 + 3x2
12x2 + 6x3
rị + 10x3
20
30
10
II)
2x1 + x2 + 5x3 = 1
2x1 + 2x2 + 2x3 = 1
4x1 + x2 = 2
III)
xị + x2 – x3 = -3
6x1 + 2x2 + 2x3 = 2
-3x1 + 4x2 + x3 = 1
(a) Use Gaussian Elimination to compute the determinants required to
solve the system using Cramer's Rule.
(b) Use Gaussian Elimination to compute the inverse of A.
(c) Use the inverse to solve the system of equations.
(d) Use Jacobi's Method to solve the system of equations. Start with a
vector of l's as initial approximation, e = 10-4. It is recommended
that you use Excel or write a program in Java to help you.
(e) Use Gauss-Seidel's Method to solve the system of equations. Start
with a vector of l's as initial approximation, e = 10-4. It is rec-
ommended that you use Excel or write a program in Java to help
you.
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