B$.$ Use the Rouch$-$Capelli Theorem by comparing the rank$(A)andrank([Ab]).$

Call the function rank$\_$comp and determine if $Ax=b$ is consistent.

Compare the result with Part A$.$ You should have the same conclusion.

Note: $r$ ank$\_$comp gives you a new command to compare if rank$(A)=$rank$([Ab]).$ When you need to use the command, read the comments in the $m-$file function first and call the function by typing the name of the function, rank$\_$comp $(A,B),$ where A and $B$ are the two input matrices.

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 include three input arguments $(n,A,Ab)$ for LS$\_$solution, where $n$ is the number of variables in the system of equations.