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Bracamonte, M. (2020). Álgebra Lineal. [Imagen]. Recuperado de http://blog.espol.edu.ec/mrbracamonte/algebra-lineal/
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A continuación, se presentan dos enunciados que son verdaderos, seleccione uno de ellos y demuéstrelo.
a) | Sea V un espacio vectorial sobre un campo \mathbb{K} y sea D un subconjunto de V linealmente independiente. Si v_0\in V es un elemento tal que v_0\notin gen(D), entonces el conjunto D\cup \{v_0\} es un conjunto linealmente independiente. |
b) | Sea (V,+,\cdot) un espacio vectorial sobre un campo \mathbb{K} de dimensión n (finita) y T:V\longrightarrow V una transformación lineal sobreyectiva. Si B=\{ v_1,v_2,...,v_3 \} es una base de V formada por vectores propios de T, entonces la matriz asociada a T en la base B es diagonal. |