Solving Ax $=$ b$30$ 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 AThe command $[$B$,$ pivcols$]=$rref$($A$)$returns B and pivcols, where matrix B $=$ rref$($A$)$ and pivcols indicates pivot columns of AThe command rank$($A$)$ returns the rank of a matrix AYou also need two m$-$file functions rank$\_$comp $($given$)$ and LS$\_$solution $($template only$).$ In these functions, you need to know:if$-$else statementIf an expression is true, it executes statements $1$ block. Otherwise, it executes statements $2$ block.if expression statements $1$ blockelse statements $2$ blockend if$-$elseif statementIf expression $1$ is true, it executes statements $1$ block. If not, check expression $2.$ If expression $2$ is true, it executes statements $2$ block. If not, execute statements $3$ block.if expression $1$ statements $1$ blockelseif expression $2$ statements $2$ blockelse statements $3$ blockend Use the reduced row echelon form $($RREF$)$ to solve Ax $=$ b$,$ where A and b are indicated in Exercise $1,$ and type your answer for the following in the Live Editor.Display the reduced row echelon form and the pivot columns of the augmented matrix $[$A b$].$Write a report to explain if there is a solution of Ax $=$ b based on rref$([$A b$]).$Verify the Rouch$-$Capelli Theorem by comparing the rank$($A$)$ and rank$([$A b$]).$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: rank$\_$comp gives you a new command to compare if rank$($A$)=$ rank$([$A b$]).$ 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$),$ in the Live Editor where A and B are the two input matrices.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, orcon$\_$with$\_$one$\_$sol if the system is consistent and has a unique solution, orcon$\_$with$\_$inf$\_$sols if the system is consistent and has infinitely many solutions.Note: You should include three inputs $($n$,$ A$,$ Ab$)$ for LS$\_$solution, where n is the number of variables in the system of equation.