C$.$ Open the template LS$\_$solution. Use the Rouch$-$Capelli Theorem as a guide and code the function using an if$-$elseif 'statement $($do not use nested if$-$else statements$).$ When LS$\_$solution is called it should return the correct system type based on whether $Ax=b$ has a solution and how many. The function should output$/$return$/$set system$\_$type to:

inc if the system is inconsistent and has no solution, or

con$\_$with$\_$one$\_$sol if the system is consistent and has a unique solution, or

con$\_$with$\_$inf$\_$sols if the system is consistent and has infinitely many solutions.

Note: You should includde three inputs $(n,A,Ab)$ for LS$\_$solution, where $n$ is the number of variables in the system of equation.