Problem on the past qualifier asks to find the value of h for which the vectors are linearly dependent:

$\displaystyle v_1=\begin{pmatrix} 1 \\ -1 \\ -3 \end{pmatrix},v_2=\begin{pmatrix} -5 \\ 7 \\ 8 \end{pmatrix},v_3=\begin{pmatrix} 1 \\ 1 \\ h \end{pmatrix}$

For vectors to be linearly dependent they need to be products of each other multiplied by some coefficient. By mental math I found that with $\displaystyle 6*v_1 + v_2 = v_3 $ vectors are linearly dependent if $\displaystyle h = -10$.

Would someone please comment on the correctness and point me to the formulaic way to find such solutions?