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Algebra Superior Rosa De Peña & Tulio Mateo Conjuntos Numéricos y Espacios Vectoriales Unidad 1 Índice 1.1 Conjuntos Numéricos …………………………………...… 1 1.2 Propiedades De Los Numeros Reales ............................... 5 1.3 Definición de Campo Numérico ........................................ 11 Espacio Vectorial………………………………………….12 Sub Espacio Vectorial…………………………………….13 1.4 Definición de Vector ........................................................... 15 1.5 El conjunto R n es una generalización de R 2 , ....................... 17 1.6 Vector Cero o Vector Nulo. .............................................. 17 1.7 Demostrar que R n define un Espacio Vectorial ................. 18 1.8 Igualdad de Vectores............................................................ 19 1.9 Vector Opuesto de un Vector Dado .................................... 19 1.10 Operaciones con Vectores ……………………………… ..19 1.10.1 Suma o Adición ………………………………… . ….. 19 1.10.2 Diferencia …………………………………………… 19 1.10.3 Producto de un Vector por un Escalar K .................... 20 1.10.4 Producto Escalar o Producto Interno o Producto Punto20 1.11 Definición de Vector Asociado ........................ …………. 21 1.12 Norma, Longitud o Tamaño de un Vector ......................... 22 1.13 Angulo entre dos Vectores ............................................... 24 1.14 Vector Unitario con el mismo sentido de un vector dado …………………………………………………………… 25 Practica Propuesta No. 1. Unidad 1…………… ... …………… .26 Practica Propues ta No. 2. Unidad 1 …………………………...29 Cuestionario Unidad No. 1 ………………………………...…36 Bibliografía Consultada ………………………………………. 37
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