Chapter 1.8, Problem 28E

In Exercises 27–28, the images of the standard basis vectors for R³ are given for a linear transformation T : R³ → R³. Find the standard matrix for the transformation, and find T(x).

$T(e_1)=\left[\begin{array}{l}2\\ 1\\ 3\end{array}\right],T(e_2)=\left[\begin{array}{l}-3\\ -1\\ 0\end{array}\right],T(e_3)=\left[\begin{array}{l}1\\ 0\\ 2\end{array}\right];x=\left[\begin{array}{l}3\\ 2\\ 1\end{array}\right]$