Answer
$\begin{bmatrix} 1 & 0&1 \\ 0 & 1&1 \\ 1&1&0 \end{bmatrix}$
Work Step by Step
We have:
$A=T( \begin{bmatrix} x\\ y \\ z\end{bmatrix} )=\begin{bmatrix} x+z\\y+z \\x+y\end{bmatrix}\\=\begin{bmatrix} x\\0\\x \end{bmatrix}+\begin{bmatrix} 0\\y\\y \end{bmatrix}+\begin{bmatrix} z\\z\\0 \end{bmatrix}\\=\begin{bmatrix} 1 & 0&1 \\ 0 & 1&1 \\ 1&1&0 \end{bmatrix}$
Thus, the required standard matrix of the linear transformation is: $A=\begin{bmatrix} 1 & 0&1 \\ 0 & 1&1 \\ 1&1&0 \end{bmatrix}$
