A$.$ 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$([Ab]).$

B$.$ Verify the Rouche$-$Capelli Theorem by comparing the rank$(A)$ and rank$([AB]).$

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: $x$ 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, $r$ ank$\_$comp$($A$,$B$).$ in the Live Editor where A and $B$ are the two input matrices.

C$.$ Open the template LS$\_$solution. Use the Rouche$-$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.