Answer
$A=T(e_1,e_2)=\begin{bmatrix}
1 & 3\\
2 & -7\\
1 & 0
\end{bmatrix}$
Work Step by Step
We are given:
$T(x_1,x_2)=(x_1+3x_2,2x_1-7x_2,x_1)$
The standard basis vectors in $R^2$ are:
$e_1=(1,0)\\
e_2=(0,1)$
Consequently,
$T(e_1)=(1,2,1)\\
T(e_2)=(3,-7,0)$
The matrix of the given transformation is:
$A=T(e_1,e_2)=\begin{bmatrix}
1 & 3\\
2 & -7\\
1 & 0
\end{bmatrix}$
