Given a $4\times 4$ rank $3$ matrix \begin{bmatrix} a_{11}&a_{12}&a_{13}&a_{14}\\ a_{21}&a_{22}&a_{23}&a_{24}\\ a_{31}&a_{32}&a_{33}&a_{34}\\ a_{41}&a_{42}&a_{43}&a_{44} \end{bmatrix} there are rationals $\alpha,\beta,\gamma,\delta\in\mathbb Q$ such that $$\alpha\cdot\mbox{row}_1+\beta\cdot\mbox{row}_2+\gamma\cdot\mbox{row}_3+\delta\cdot\mbox{row}_4=0$$ holds.
How to find these rationals $\alpha,\beta,\gamma,\delta\in\mathbb Q$?