Define two linear transformations, $\ltdefn{T}{\complex{4}}{\complex{3}}$ and $\ltdefn{S}{\complex{3}}{\complex{2}}$ by \begin{align*} \lt{S}{\colvector{x_1\\x_2\\x_3}} &= \colvector{ x_1-2x_2+3x_3\\ 5x_1+4x_2+2x_3 } & \lt{T}{\colvector{x_1\\x_2\\x_3\\x_4}} &= \colvector{ -x_1+3x_2+x_3+9x_4\\ 2x_1+x_3+7x_4\\ 4x_1+2x_2+x_3+2x_4 } \end{align*} Using the proof of Theorem MLTCV compute the matrix representations of the three linear transformations $T$, $S$ and $\compose{S}{T}$. Discover and comment on the relationship between these three matrices.