(Solved): Write the solution set of the given homogeneous system in parametric vector form. \( 2 x_{1}+2 x_{2 ...

Write the solution set of the given homogeneous system in parametric vector form. \( 2 x_{1}+2 x_{2}+4 x_{3}=0 \) \( -6 x_{1}-6 x_{2}-12 x_{3}=0 \) \( -4 x_{2}+12 x_{3}=0 \) where the solution set is \( x=\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}\right] \) \[ x=x_{3} \] (Type an integer or simplified fraction for each matrix element.)