Answer
$T(x_1,x_2,x_3)= (2x_1-x_2+5x_3,3x_1+x_2-2x_3)$
Work Step by Step
We are given:
$A=\begin{bmatrix}
2 & -1 & 5\\
3 & 1 & -2
\end{bmatrix}$
Since $T=Ax$, the linear transformation is:
$T(x_1,x_2)=\begin{bmatrix}
2 & -1 & 5\\
3 & 1 & -2
\end{bmatrix}\begin{bmatrix}
x_1\\
x_2 \\
x_3
\end{bmatrix}\\
\rightarrow T(x_1,x_2,x_3)= (2x_1-x_2+5x_3,3x_1+x_2-2x_3)$