Let $T$:$R^3{R}^2$ be defined by $T(\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right])=\left[\begin{array}{c}4x_1-x_2\\ 3x_3\end{array}\right].$

Let $B=\{u_1=\left[\begin{array}{c}6\\ -6\\ -3\end{array}\right],u_2=\left[\begin{array}{c}7\\ -5\\ 3\end{array}\right],u_3=\left[\begin{array}{c}-2\\ -1\\ 2\end{array}\right]\}$ and $C=\{v_1=\left[\begin{array}{c}4\\ -7\end{array}\right],v_2=\left[\begin{array}{c}6\\ 7\end{array}\right]\}$

What augmented matrix should be used to find $[T{]}_B^C,$ the matrix representation of $T$ with respect to the bases $B$ and $C.$