\[S : C^2 => C^3\]
\[\\S(\left[\begin{array} {rrr} x1 \\ x2 \end{array}\right]) = \left[\begin{array} {rrr} 3x1 + 5x2 \\ 8x1 -3x2\\ -4x1 \end{array}\right] \] #### Matrics representation of Linear Transformation.
\[\\\left[\begin{array} {rrr} x1 \\ x2 \end{array}\right] \left[\begin{array} {rrr} 3 & 5 \\ 8 & -3 \\ -4 & 0 \end{array}\right]\]