\begin{bmatrix} x' \\ y' \\ z' \end{bmatrix} = \begin{bmatrix} -k \\ k-y \\ k+y \end{bmatrix} = \begin{bmatrix} -1 & 0 & 0 \\ 1 & -1 & 0 \\ 1 & 1 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = Ax
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