Burton Carlson
06/04/2024 · High School
6.- Determine si los conjuntos con sus operaciones definidas, es un espacio vectorial. \[ \begin{array}{l}\left(x_{1}, y_{1}, z_{1}\right) \oplus\left(x_{2}, y_{2}, z_{2}\right)=\left(x_{1}+x_{2}, y_{1}+y_{2}, z_{1}+z_{2}\right) \\ \alpha \odot(x, y, z)=(\alpha x, \alpha y, \alpha z)\end{array} \]
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Para verificar si el conjunto con las operaciones dadas es un espacio vectorial, se deben cumplir las propiedades de cierre bajo la adición, asociatividad, existencia de un vector cero, existencia de inversos, cierre bajo la multiplicación por escalares, y distributividad. Se verifican estas propiedades para las operaciones dadas.
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