library(pracma)\[\mathbb{C}^3 \rightarrow \mathbb{C}^4, T\left \{\begin{array}{r} x \\ y \\ z \\ \end{array} \right \} = \left \{\begin{array}{r} 3x+2y+z \\ x+y+z \\ x-3y \\ 2x+3y+z\\ \end{array} \right \}\]
\[\left[\begin{array}{rrr} 3 & 2 & 1\\ 1 & 1 & 1\\ 1 & -3 & 0 \\ 2 & 3 & 1\\ \end{array} \right]\]