For which value of $k$ the vector $u=\left[\begin{array}{c}1\\ -2\\ k\end{array}\right]$ is a linear combination of the vectors ${v}_{1}=\left[\begin{array}{c}3\\ 0\\ -2\end{array}\right]$ and ${v}_{2}=\left[\begin{array}{c}2\\ -1\\ -5\end{array}\right]$ .