Find all solutions to the system using the Gauss$-$Jordan elimination algorithm.

$-4x_1+4x_2-2x_3=0$

$4x_1-12x_2+4x_3=0$

$-4x_1+4x_2-2x_3=0$

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The system has a unique solution. The solution is $x_1=,x_2=,x_3=.$

B$.$ The system has an infinite number of solutions characterized by $x_1=,x_2=x_1=x_2=s,x_3=t,-.$

$D.$ The system has $no$ solution.$x_3=s,-.$

$C.$ The system has $an$ infinite number $of$ solutions characterized $by{x}_1=x_2=s,x_3=t,-.$

$D.$ The system has $no$ solution.