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