Answer
$T(x_1,x_2)= (x_1+3x_2,-4x_1+7x_2)$
Work Step by Step
We are given:
$A=\begin{bmatrix}
1 & 3\\
-4 & 7
\end{bmatrix}$
Since $T=Ax$, the linear transformation is:
$T(x_1,x_2)=\begin{bmatrix}
1 & 3\\
-4 & 7
\end{bmatrix}\begin{bmatrix}
x_1\\
x_2
\end{bmatrix}\\
\rightarrow T(x_1,x_2)= (x_1+3x_2,-4x_1+7x_2)$
