Find the $3 \times 3$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} y \\ z \\ x + y + z \end{pmatrix}\]for all real numbers $x,$ $y,$ and $z.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the $3 \times 3$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} y \\ z \\ x + y + z \end{pmatrix}\]for all real numbers $x,$ $y,$ and $z.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \end{pmatrix}
Find the $3 \times 3$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} y \\ z \\ x + y + z \end{pmatrix}\]for all real numbers $x,$ $y,$ and $z.$
train