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AM2060 Assignment 2024
Kieran Mulchrone
October 16, 2024
This assignment is worth 20% of your final grade in this module
Please state in your code that this is entirely your own work.
1 Introduction
You are to implement Gaussian elimination to solve systems of linear equations in C#.
2 Specific requirements
1. Create a class called GaussEliminate which implements the algorithm. Your code must include the following methods:
(a) void SetAb(double [,] A, double [] b); //allows the user to specify the problem to be solved.(b) double [] Solve(); //solves the problem, outputs the formatted answer to screen and returns the answer to an array.(c) void DisplayAugMatrix(); //outputs the Augmented matrix to the screen in an easy to read and well formatted way.(d) Implement partial pivoting and scaled partial pivoting (see the notes on can vas). Can you think of a way to allow the user to choose the method of solution i.e. no pivoting, partial pivoting or scaled partial pivoting?(e) Your code should be able to deal with a zero in the pivot position.(f) Your code should work for systems of equations of dimension 2 or higher.
2. Try to deal with all potential errors e.g. making sure matrices and vectors are correctly sized.
3. Keep your code tidy and readable. Put in a reasonable amount of comments but no essays. Comments should help the reader understand your code.
4. I will test your code by running code like the following against it:
GaussEliminate g = new GaussEliminate();
double [,] A1= new double[4,4]{{10,1,1,1},{1,1,2,3},{-1,1,2,1},{3,2,-1,0}};
double [] b1 = new double[4] {1,2,-10,1};
g.SetAb(A1,b1);
g.Solve();
double [,] A2= new double[3,3]{{5,1,2},{-3,9,4},{1,2,-7}};
double [] b2 = new double[3] {10,-14,-33};
g.SetAb(A2,b2);
g.Solve();
5. You are only required to submit the file containing the code for the GaussEliminate class, i.e. a code file ending in .cs.