$30$ Points $[10$ Points Per Part$]$

In this exercise, you use the RREF and Rouch$$Capelli Theorem to determine if $Ax=b$ is consistent. You may need the following commands for this exercise.

The command rref $($A$)$ returns the reduced row echelon form of a matrix $A$

The command $,$ pivcols$]=$rref $($A$)$ returns $B$ and pivcols, where matrix $B=$rref$(A)$ and pivcols indicates pivot columns of A

The command rank$(A)$ returns the rank of a matrix $A$

You also need two m$-$file functions rank$\_$comp $($given$)$ and LS$\_$solution $($template only$).$ In these functions, you need to know:

if$-$else statement

If an expression is true, it executes statements $1$ block. Otherwise, it executes statements $2$ block.

if expression