Find the $2 \times 2$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 3 \\ 0 \end{pmatrix}\]and
\[\mathbf{M} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 \\ -7 \end{pmatrix}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the $2 \times 2$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 3 \\ 0 \end{pmatrix}\]and
\[\mathbf{M} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 \\ -7 \end{pmatrix}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} 3 & 2 \\ 0 & -7 \end{pmatrix}
Find the $2 \times 2$ matrix $\mathbf{M}$ such that
\[\mathbf{M} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 3 \\ 0 \end{pmatrix}\]and
\[\mathbf{M} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 \\ -7 \end{pmatrix}.\]
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