In this project, you are required to implement a system of linear equations solver based on Cramer's Rule in MIPS assembly language using MARS simulator.

To refresh your memory about Cramer's rule, check this website: Cramer's rule $($math$.$net$)$

Here are the specifications of the solver you are required to implement:

$1.$ For simplicity, your solver supports systems of linear equations with two or three variables only

$2.$ The linear equations are read from an input text file.

$3.$ The program should prompt the user to enter the input file name or path

$4.$ The input file can contain multiple systems of linear equations separated by empty lines

$5.$ The program should validate the input file and the structure of the systems of the linear equations, and print the appropriate error messages, when required

$6.$ The menu should remain in an infinite loop until the user decides to exit by entering $\text{'}$e$\text{'}$ or $\text{'}$E$\text{'}$

$7.$ The program prompts the user to choose how they would like the results to be displayed: either in an output text file or on the screen

a$.$ If the user enters $\text{'}$ f $\text{'}$ or $\text{'}\backslash ($ F $\backslash )\text{'},$ then the results will be saved to an output text file

b$.$ If the user enters $\text{'}$s$\text{'}$ or $\text{'}$S$\text{'},$ then the results will be printed on the screen

c$.$ If the user enters anything else, an invalid input error message is display on the screen.

$8.$ Solutions for different systems of equations can be separated by empty lines

Example:

Given the following snapshot of the input text file

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$2$ x$+3$ y$+$z$=5\backslash \backslash$

$4$ x$+2$ y$+2$ z$=8\backslash \backslash$

x$+$y$+2$ z$=6\backslash \backslash$

x$+$y$=5\backslash \backslash$

$2$ x$+$y$=10$

$\backslash$end$\{$array$\}$

$\backslash ]$

Then the output should be as follows

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$\backslash$mathrm$\{$X$\}=1/2\backslash \backslash$

$\backslash$mathrm$\{$Y$\}=1/2\backslash \backslash$

$\backslash$mathrm$\{$Z$\}=5/2$

$\backslash$end$\{$array$\}$

$\backslash ]$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

X$=5\backslash \backslash$

Y$=0$

$\backslash$end$\{$array$\}$

$\backslash ]....$full complete run code