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.