Compute the matrix representation of $T$ relative to the bases $B$ and $C$. \begin{align*} \ltdefn{T}{P_3}{\complex{3}},\quad \lt{T}{a+bx+cx^2+dx^3}= \colvector{2a-3b+4c-2d\\a+b-c+d\\3a+2c-3d}\\ B=\set{1,\,x,\,x^2,\,x^3}\quad\quad C=\set{\colvector{1\\0\\0},\,\colvector{1\\1\\0},\,\colvector{1\\1\\1}} \end{align*}