(Solved): Write the solution set of the given homogeneous system in parametric vector form. \[ \begin{array}{ ...

Write the solution set of the given homogeneous system in parametric vector form. \[ \begin{array}{l} 3 x_{1}+3 x_{2}+6 x_{3}=0 \\ -6 x_{1}-6 x_{2}-12 x_{3}=0 \\ -3 x_{2}-3 x_{3}=0 \\ \text { where the solution set is } \mathrm{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right] \\ \end{array} \] \[ x=x_{3}\left[\begin{array}{r} -3 \\ 3 \\ 1 \end{array}\right] \] (Type an integer or simplified fraction for each matrix element.)