Show that the following vectors are linearly dependent. $$ |v_1\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, |v_2\rangle = \begin{pmatrix} -1/2 \\ \sqrt{3}/2 \end{pmatrix}, |v_3\rangle = \begin{pmatrix} 3/2 \\ \sqrt{3}/2 \end{pmatrix} $$
Which of the following choices of coefficients satisfy the linear dependence of the three vectors $$ a_1 |v_1\rangle + a_2 |v_2\rangle + a_3 |v_3\rangle = 0 $$