The following systems of equations is easy to solve 2x+ y = 18 3x + 2y = 30 by g

Question

The following systems of equations is easy to solve

2x+ y = 18

3x + 2y = 30

by graphing, by substitution, or elimination.The solution (6,6) is easily arrived at using a graphing calculator using matrix algebra to solve the matrix equation.

Ax=b

A= 2 1        A^-1 = 2 -1     b = 18               A^-1b= [2 -1] * [18]  = [6]

     3 2                  -3  2          30                          [-3 2]     [30]     [6]

The literature contains numerous algorithms for solving ill conditioned systems.In order to illustrate the shortfalls of floating point arithmetic for this projects you will limited to algorithms implementing the gauss- jordan method.

A.) Write a java program that uses an algorithm implementing the Gauss- jordan method to solve the system of linear equations given in the introduction.Your output must show the output of every calculation to no more than 7 decimal places.You must create and use a function that cuts off the result of each calculation at exactly seven decimal places and uses this cutoff value in any susbsequesnt calculation.

B.) Use the following ten step procedure to solve the problem:

1)Problem

2)Input

3)Output

4)Discussion

5)Assumptions

6)Top Down Design

7)Variables

8)Pseudocode

9)Flowchart

10)a Java source code

  b) program output

Explanation / Answer

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