Consider the system of linear equations

$x-y=2$

$kx-y=k$

$($a$)$ Reduce the augmented matrix for this system to row$-$echelon $($or upper$-$triangular$)$

 

form. $($You do not need to make the leading nonzero entries $1.)$ 

 

$($b$)$ Find the values of $k($if any$)$ when the system has

i$.$ no solutions,

ii$.$ exactly one solution $($if this is possible, find the solution in terms of $k),$

iii. infinitely many solutions $($if this is possible, find the solutions$).$