Solutions to a system of linear equations

Question

earlier in the question I was required to convert an augmented matrix to its row-reduced echelon form. I ended up with this:

$$ \left[\begin{array}{rrr|r} 1 & 2 & -1 & -3 \\ 0 & 1 & -k-3 & -5 \\ 0 & 0 & k^2-2k & 5k+11 \end{array}\right] $$

the question I'm stuck on asks: For what value(s) of k does the system have

. no solutions

. a unique solution

. infinitely many solutions

Answer 1

The system has no solution if : k =2 or k =0 ,and k not= -11/5 the system has unique solution if : K does not have any of these values 2 or 0 and -11/5 . that's for all value except 2,0,-11/5 and the system i think does not have infinitely many solutions because then k should have two different values simultanously and i have some doubt about the unique solution also .