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UBA - CienciaS • Ver Tema - Segundo Parcial - 09/12/08
UBACS Q&A Foro WikiCS
Fecha actual 22 Jun 2024, 16:53

Todos los horarios son UTC - 3 horas




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Autor Mensaje
 Asunto: Segundo Parcial - 09/12/08
NotaPublicado: 31 Dic 2008, 17:21 
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Registrado: 16 May 2008, 22:21
Mensajes: 194
Ubicación: Pilar, Bs. As.
Dejo los enunciados..

1. Sea : la transformación lineal definida por y sea : un endomorfismo tal que
, doinde es la base canónica de .
Decidir si existe un isomorfismo : tal que .

2. (a) Hallar la matriz en la base canónica de un producto interno : para el cual se satisfacen simultáneamente
, , .
Las siguientes tres rectas son ortogonales: , y la recta que pasa por los puntos y .

(b) Para el producto interno calculado en (a), encontrar el subespacio ortogonal al vector .

3. Sea y . Hallar una transformación ortogonal : tal que .

4. Sea : la forma bilineal definida por . Hallar una base de tal que
.

5. Sean dos matrices con todos sus autovalores reales y positivos y tales que es semejante a . Probar que y son semejantes.

JUSTIFIQUE TODAS SUS RESPUESTAS ( :P )


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Todos los horarios son UTC - 3 horas


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