Answer
$\begin{bmatrix} 1 & -1&1 \\ 2 & 1&-3 \end{bmatrix}$
Work Step by Step
We have:
$A=T( \begin{bmatrix} x\\ y \\ z\end{bmatrix} )=\begin{bmatrix} x-y+z\\2x+y-3z \end{bmatrix}\\=\begin{bmatrix} x\\ 2x \end{bmatrix}+\begin{bmatrix} -y\\y \end{bmatrix}+\begin{bmatrix} z\\-3z \end{bmatrix}\\=\begin{bmatrix} 1 & -1&1 \\ 2 & 1&-3 \end{bmatrix}$
Thus, the required standard matrix of the linear transformation is: $A=\begin{bmatrix} 1 & -1&1 \\ 2 & 1&-3 \end{bmatrix}$
