Algebra Archive: Questions from March 17, 2023
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Example 7. Let \( \mathrm{V}=\{(x, y): x, y \in \mathbf{R}\} \). Show that \( V_{\mathbf{R}} \) is not a vector space under the following operations : (i) \( (x, y)+(\pi, t)=(x, y) \) and \( \alpha(x,2 answers -
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14. Prove or give a counterexample: For a function \( F: X \rightarrow Y \), if \( A, B \subseteq X \) then \( F(A) \subseteq F(B) \)2 answers -
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Verificar que el conjunto \( S=\{(1,1,0),(1,0,1),(1,1,1)\} \) genera a \( R^{3} \). Determine si el siguiente subconjunto de \( \mathrm{P}_{2} \) es linealmente dependiente o linealmente independient2 answers -
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