Write a script GaussElimination.m in which

$(1)$ the user is prompted to enter a system of linear equations in augmented

matrix form $(\backslash$times $(+1),$ where $$ is arbitrary$)$

$(2)$ the script obtains the solution of the linear system via Guass$-$Jordan

elimination using functions that implement elementary row operations

$(3)$ the script finally outputs the solution

The script should be broken into $4$ main parts:

Part $1$: Prompts the user for the augmented system and calculates the number of

rows and columns. The number of columns should be $1$ greater than

the number of rows, otherwise the script should give an error message.

Part $2$: If the system entered by the user is valid, the second part reduces

the system to upper triangular form following the algorithm discussed

in the tutorial making use of functions linearcomb and swap

Part $3$: Next the system is further reduced to lower triangular. The algorithm

for this part should be the mirror image of the algorithm in Part $2$

Part $4$: Now that the system is purely diagonal, divide each row of the system

by its diagonal entry to obtain the solution. Output the solution.