(Solved): A linear transformation \( T \) is given below. Find \( [T] \) \[ T\left(\left[\begin{array}{l} x_ ...

A linear transformation \( T \) is given below. Find \( [T] \) \[ T\left(\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]\right)=\left[\begin{array}{c} x_{1}+2 x_{2}-3 x_{3} \\ x_{2} \\ 0 \\ 3 x_{1}-2 x_{2}-7 x_{3} \end{array}\right] \] \[ [T]=? \]