Word Count : 447

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आपके द्वारा दी गई समीकरण \( x + y - z = 0 \) को हल करने के लिए हमें यह जांचना है कि \( W = \{(x, y, z) \in \mathbb{R}^3 \mid x + y - z = 0\} \) उपसमष्टि (subspace) है या नहीं। किसी भी सेट को उपसमष्टि (subspace) माना जाता है अगर वह निम्नलिखित तीन शर्तों को पूरा करता है: 1. शून्य वेक्टर का सदस्य होना चाहिए - \( \mathbf{0} = (0, 0, 0) \) को \( W \) में होना चाहिए। 2. समीकरणों का क्लोजर - यदि \( \mathbf{v}_1 \) और \( \mathbf{v}_2 \) \( W \) में हैं, तो \( \mathbf{v}_1 + \mathbf{v}_2 \) भी ________ _______ _________ ___ ____ ________ ____ _________ _____ ___.
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