Answer
$T(x_1,x_2,x_3,x_4,x_5)= (x_1-4x_2-6x_3+2x_5)$
Work Step by Step
We are given:
$A=\begin{bmatrix}
1 & -4 & -6 & 0 & 2\\
\end{bmatrix}$
Since $T=Ax$, the linear transformation is:
$T(x_1,x_2,x_3)=\begin{bmatrix}
1 & -4 & -6 & 0 & 2\\
\end{bmatrix}\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
x_4 \\
x_5
\end{bmatrix}\\
\rightarrow T(x_1,x_2,x_3,x_4,x_5)= (x_1-4x_2-6x_3+2x_5)$
