The command rref $($is$)$ returns the reduced row echelon form of a matrix $A_1$

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

columns of $A_2$

The command rank $(A)$ returns the rank of a matrix $A_2$

You also need two $m-$fle functions rank$\_$comp $($given$)$ and Ls$\_$solut ion $($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$-$elseif statement

If 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 $1$ block

elseif expression $2$

statements $2$ block

eise

statements $3$ block

$x{a}^{\text{'}}$

following in the Live Editor.

Display the reduced row echelon form and the pivot columns of the augmented matrix $A_{l}b.$

Write a report to explain if there is a solution of $x=b$ based on rref $[(,b]).$

B$.$ Use the Rouch$-$Capelli Theorem by comparing the rank$()$ and rank$(\{$:$[{}_{i}b]).$

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

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

Note: rank$\_$comp gives you a new command to compare if rank$({}_1)=$rank$([{}_{1}b]).$ When you need to use the command, read the

the two input matrices.

C$.$ Open the template Ls$\_$solut ion. Use the Rouch$-$Capelli Theorem as a guide and code the function using an if$-$elseif statement ido

not use nested if$-$else statements$).$ When Ls$\_$solut ion is called it should return the correct system type based on whether $x=b$

has a solution and how many. The function should output$/$return$/$set systern$\_$type to:

inc ir 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 infitely many solutions.

Note: You should include three input arguments $)$ for Ls$\_$solut ion, where $n$ is the number of variables in the system of

equations. Code I have so far:$\%---$ Part A $[10$ Points$]---\%$

Ab $=[$A$,$ b$]$; $\%($WRITE COMMAND BEFORE SEMI$-$COLON$)$

$\%($COMMENTS FOR B AND pivcols$)$

$[$B$,$ pivotcol$]=$ rref$($Ab$)$;

disp$(\text{'}$Reduced Row Echelon Form $($RREF$)$:$\text{'})$;

disp$($B$)$;

disp$(\text{'}$Pivot Columns:$\text{'})$;

disp$($pivotcol$)$;

$\%($EXPLAIN WHY SYSTEM IS INCONSISTENT$)$

$\%---$ Part B $[10$ Points$]---\%$

rank$\_$A $=$ rank$($A$)$;

rank$\_$Ab $=$ rank$($Ab$)$;

rank$\_$comp$($rank$\_$A$,$ rank$\_$Ab$)$;

if rank$\_$A $==$ rank$\_$Ab

disp$(\text{'}$The system Ax $=$ b is consistent.$\text{'})$;

if rank$\_$A $==$ n

disp$(\text{'}$The system has a unique solution.$\text{'})$;

else

disp$(\text{'}$The system has infinitely many solutions.$\text{'})$;

end

else

disp$(\text{'}$The system Ax $=$ b is inconsistent.$\text{'})$;

end

$\%($STATE THEOREM$)$

$\%($APPLY$/$USE THEOREM & COMPARE TO RESULT FROM PART A$)$

$\%---$ Part C $[10$ Points$]---\%$

LS$\_$solution$($n$,$ A$,$ Ab$)$;

$[$m$,$ n$]=$ size$($E$)$; $\%($UNCOMMENT LINE AND COMPLETE$)$

solution$\_$type $=$NaN;

end I am getting an error that there is no variable n as it is called in the function. How would I implement n$?$ Here is the function I wrote. LS$\_$solution$($n$,$ A$,$ Ab$)\%($PURPOSE OF FUNCTION$)$

$\%$ n $=$ number of variables

$\%$ A $=$ coefficient matrix

$\%$ Ab $=$ augmented matrix $[$A b$]$

inc $=$ "Inconsistent";

con$\_$with$\_$one$\_$sol $=$ "Consistent with One Solution";

con$\_$with$\_$inf$\_$sols $=$ "Consistent with Infinite Solutions";

rank$\_$A $=$ rank$($A$)$;

rank$\_$Ab $=$ rank$($Ab$)$;

$\%$ Add your code below

if rank$\_$A $$ rank$\_$Ab

system$\_$type $=$ inc;

elseif rank$\_$A $==$ rank$\_$Ab

if rank$\_$A $==$ n

system$\_$type $=$ con$\_$with$\_$one$\_$sol;

else

system$\_$type $=$ con$\_$with$\_$inf$\_$sols;

end I need help with the parts under the comments and anything that says NaN or to explain something. In essence, if it has a comment then I need help.