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