Answer
$T(x_1,x_2,x_3)= (2x_1+2x_2-3x_3,4x_1-x_2+2x_3,5x_1+7x_2-8x_3)$
Work Step by Step
We are given:
$A=\begin{bmatrix}
2 & 2 & -3\\
4 & -1 & 2 \\
5 & 7 & -8
\end{bmatrix}$
Since $T=Ax$, the linear transformation is:
$T(x_1,x_2,x_3)=\begin{bmatrix}
2 & 2 & -3\\
4 & -1 & 2 \\
5 & 7 & -8
\end{bmatrix}\begin{bmatrix}
x_1\\
x_2 \\
x_3
\end{bmatrix}\\
\rightarrow T(x_1,x_2,x_3)= (2x_1+2x_2-3x_3,4x_1-x_2+2x_3,5x_1+7x_2-8x_3)$