Chapter 1.8, Problem 27E

In Exercises 27–28, the images of the standard basis vectors for R³ are given for a linear transformation $T:R^3\to R^3$. Find the standard matrix for the transformation, and find T(x).

$T(e_1)=\left[\begin{array}{l}1\\ 3\\ 0\end{array}\right],T(e_2)=\left[\begin{array}{l}0\\ 0\\ 1\end{array}\right],T(e_3)=\left[\begin{array}{l}4\\ -3\\ -1\end{array}\right];x=\left[\begin{array}{l}2\\ 1\\ 0\end{array}\right]$