Word Count : 378

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Consider the group (SP_2(\mathbb{R})), which consists of (2 \times 2) real matrices (M) satisfying (M^T J M = J), where [ J = \begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}. ] We want to show that (SP_2(\mathbb{R})) acts transitively on (\mathbb{R}^2 \setminus {\mathbf{0}}). Let (\mathbf{v} = \begin{pmatrix} x \ y \end{pmatrix} \in \mathbb{R}^2 \setminus {\mathbf{0}}). Our goal is to find (M ___ _______ ___ ___ ______.
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