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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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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.
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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