Answer
$A=\begin{bmatrix}
3 & -2\\
1 & 5
\end{bmatrix}$
Work Step by Step
We are given:
$T(x_1,x_2)=(3x_1-2x_2,x_1+5x_2)$
The standard basis vectors in $R^2$ are:
$e_1=(1,0)\\
e_2=(0,1)$
Consequently,
$T(e_1)=(3,1)\\
T(e_2)=(-2,5)$
The matrix of the given transformation is:
$A=T(e_1,e_2)=\begin{bmatrix}
3 & -2\\
1 & 5
\end{bmatrix}$
