III Parcial ord CAL II-2016.pdf - Instituto Tecnol´ogico de Costa Rica Escuela de Matem´atica ´ MA-1103 C´alculo y Algebra Lineal Tiempo m´aximo 2

III Parcial ord CAL II-2016.pdf - Instituto Tecnol´ogico...

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Instituto Tecnol´ ogico de Costa Rica Tiempo m´ aximo: 2 horas y 15 minutos Escuela de Matem´ atica Puntaje m´ aximo: 35 puntos MA-1103 C´alculo y ´ Algebra Lineal II semestre 2016 II Examen parcial Instrucciones: Esta es una prueba de desarrollo, por lo tanto, debe presentar todos los pasos y procedimientos que le permitieron obtener cada una de las respuestas. Trabaje en forma clara, ordenada y utilice bol´ ıgrafo para resolver el examen. No son procedentes las apelaciones que se realicen sobre ex´amenes resueltos con l´ apiz, lapiceros de tinta borrable o que presenten alg´un tipo de alteraci´ on. No se permite el uso de calculadora programable ni el uso dispositivos electr´ onicos con memoria de texto o conectividad inal´ ambrica. 1. Sea { u , v , w , a } un conjunto linealmente independiente de un espacio vectorial IR n . Determine si el conjunto { X , Y , Z } es linealmente independiente o linealmente dependiente si se sabe que: X = u + v + 2w , Y = a - v , Z = v + w . (4 puntos) 2. Determine los vectores P y Q en IR 3
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