Exercise 6

Consider the vectors $$\vvec_1=\left[\begin{array}{r} 3 \\ -1 \\ 1 \end{array}\right], \vvec_2=\left[\begin{array}{r} 1 \\ 1 \\ 2 \end{array}\right].$$ For what value(s) of $k$, if any, can the vector $\left[\begin{array}{r} k \\ -2 \\ 5 \end{array}\right]$ be written as a linear combination of $\vvec_1$ and $\vvec_2$?