Row Reduction & Rank · Medium problem

Three instruments measure combinations of two unknown quantities $p,q,r$: instrument 1 reads $p+2q-r$, instrument 2 reads $2p-q+3r$, and instrument 3 reads $5p+kq+r$. If instrument 3's reading always equals some fixed combination of instruments 1 and 2's readings (for every $p,q,r$), it adds no new information. Find the value of $k$ for which that happens.