Word Count : 378

---

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 _________ __________ _________ _____ _________ _____ __________ _________.
_____ ________ ____ ________ ____.
______ ___ _________ ____ _________ _____ _______ ___.
___ ______ ___ __________ ___ __________ ________ __________ ______.
____ ________ ___ ___ _______ ______ __________ __________ ________ __________ ______ ___.
_____ __________ _________ ______ ___ _________ ____.
____ ________ ______ _______ __________ ___ ___.
__________ __________ _______ ______ ________ _______ _______ ________ ____ __________.
________ ___ __________ ______ _____.
______ __________ ______ ____ ____ _______ ______ ___ _____ _____.
________ ____ ______ _____ ________ ________ _____ ______ __________ ______ _________ _______.
_______ __________ _____ ___ ______ ________ __________ ______ ________ _______ _________ _______.
_______ __________ __________ _______ _____ ____ _______.
______ ______ _________ ___ __________ _________ ______ ________ ______ ____ ______.
_______ _______ ____ _________ _________.
____ _________ _____ _________ ______ ___ _______ ___ ______ _____ _______ __________.
______ _______ __________ ______ _____ _________ __________ __________ ________.
______ ________ _____ _________ _________ ______ ______ ___.
___ ______ _________ ________ ____ _____ ____.
______ _________ _______ ___ _____ _____ ___ ___ ___ _______.
________ ___ ______ _______ ______ ______ ______ _________ _____.
___ _____ ________ _______ _________ _____ ______.
__________ ________ ______ ______ ___ _________ _________.
__________ ______ ______ _______ _______ ______ ______ __________ ___ ___ _____.
_________ __________ ___ _______ _____ _______ __________ ________.
____ ___ _________ ______ __________.
__________ ___ __________ ______ _________ ____ ______ _______ _______ _________ _____.
_________ ___ ___ __________ ________ __________ ______ __________ _________ ____ _________ _______.
________ ___ __________ _____ _____ ______ ____ _____ ___ ______ __________ ______.
_________ __________ _______ ____ ________ _______ __________ _______.
___ _______ _______ _________ __________ ________ _________ ____ _____ ____ ____ _____.
______ ___ _________ ____ ___ ________ __________.
_________ ______ __________ ______ _____ _______.
________ _______ _________ ____ _______ __________.
__________ ______ ______ _________ ____ _____ __________.
_______ ___ ____ ______ ______ ____ _____ _____ __________.
_____ __________ _______ ______.
Get Full Answer on WhatsApp