Word Count : 260

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कोई रूपांतरण \( T: \mathbb{R}^2 \to \mathbb{R}^2 \) रैखिक होता है यदि यह निम्नलिखित दो गुणों को संतुष्ट करता है: 1. ऐडिटिविटी (संगति): \[ T(\mathbf{u} + \mathbf{v}) = T(\mathbf{u}) + T(\mathbf{v}) \quad \text{सभी } \mathbf{u}, \mathbf{v} \in \mathbb{R}^2 \text{ के लिए।} \] 2. होमोमॉर्फिज्म (स्केलर गुणन के प्रति संगति): \[ T(c \mathbf{u}) = c T(\mathbf{u}) \quad \text{सभी } c \in \mathbb{R}, \mathbf{u} \in \mathbb{R}^2 \text{ ______ _______ _____ ________ _________ ________ _______ ___ _______ ________ ______ _______.
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