Let $X=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ and $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right]$. For $\mathrm{k} \in N$, if $X^{\prime} A^{k} X=33$, then $\mathrm{k}$ is equal to _______.