Implement a set of functions in python to analyze and solve linear systems. Before starting, read the

document on Piazza $$Linear Algebra in Python.$$

Solving a linear system using Gaussian Elimination requires implementing three functions:

$($a$)$ forward elmination $($Stage $1)$

$($b$)$ testing for consistency

$($c$)$ backsubstitution $($Stage $2)$

I have written the code for forward elimination. Your job is to provide the rest of the code and use the resulting

set of functions to analyze some linear systems. $($In case it helps, the code you have to write is $($quite a bit$)$

shorter than the code I have already supplied!$)$

In hw$2$GECode.py I have provided the function:

forwardElimination$($B$)$

which takes a matrix $($numpy array$)$ B and returns a new matrix that is the row echelon form of B$.$ There are also

helper functions in that file, for doing things like swapping rows of a matrix, doing row reduction, etc.

You need two write two functions:

inconsistentSystem$($B$)$

which takes a matrix B in echelon form, and returns True if it represents an inconsistent system, and False

otherwise; and

backsubstitution$($B$)$

which returns the reduced row echelon form matrix of B$.$

Using these, you should be able to analyze a matrix representing a linear system as follows:

AEchelon $=$ forwardElimination$($A$)$

if $(!$ inconsistentSystem$($AEchelon$))$:

AReducedEchelon $=$ backsubstitution$($AEchelon$)$

and then by inspecting AReducedEchelon you should be able to write down the solution set for the linear

system.