Examen de algebra lineal 8
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Examen de algebra lineal 8

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Examen de algebra lineal 8 Examen de algebra lineal 8 Document Transcript

  • ESCUELA POLITÉCNICA NACIONALExamen Supletorio de Álgebra Lineal1. Sea: P(t) →( ) ( ( )) ( ( ) ( ))a) Determinar una base para el N(f)b) Indicar cuál es la dimensión de la Img (f).( )( )1. P(t) →( ) ( ( )) ( ( ) ( ))*( ) ( ) ( )+*( ) ( ) ( )+*( ) ( ) ( )+*( ) ( ) ( )+{⟨ | | ⟩ ⟨ | | ⟩ ( ) ⟨ | | ⟩⟨ | | ⟩*( ) +*( )+( )B genera a W8
  • ESCUELAPOLITÉCNICANACIONAL→ B es base de Nf*( ) +*( ) ( ) +* ( ) ( ) +*( ) ( ) +
  • ESCUELAPOLITÉCNICANACIONAL2. Sea: ( ) →Tal que: , - = ( )Donde *( ) ( ) ( )+Hallar f( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ){. | /{( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( )
  • ESCUELAPOLITÉCNICANACIONAL3. Sea: , - = . / matriz asociada a: f: → ( )Donde C1 y C2 son las bases canónicas. Determinar: ¿f es inversible?Hallar( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ){. | /{( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )Inversa:*( ) ( ) ( )+*( ) ( ) ( ) ( )+{. | / . | / ( ) . | / . | /{*( ) +*( )+Es inyectiva
  • ESCUELAPOLITÉCNICANACIONALEs sobreyectiva→f es Biyectiva→→f es Inversibleb){. | / . | / ( ) . | / ( | ){( )( ) ( ) ( )
  • ESCUELAPOLITÉCNICANACIONAL4. Sea:A= ( )a) Hallar los valores propios.b) Vectores propios.c) Encontrar una base ortonormal.| A-α I | = 0| | | | | |( )( )( )a) 1) -3- = 0 2) 5- 3) -4-b)Sea( | ) ( | ) ( | ) ( | )( | )* ( ) +* ( ) +* ( ) +* ( )+
  • ESCUELAPOLITÉCNICANACIONALSea( | ) ( | )( | ) ( | )( | )* ( ) +* ( ) +* ( ) +* ( )+Sea( | ) ( | ) ( | )* ( ) +* ( ) +* ( ) +* ( )+c)-> *( ) ( ) ( ) +( )( )( ) ( )( ) ( )( )
  • ESCUELAPOLITÉCNICANACIONAL(37/9, 8, -29/9)( )( ) ( )( ) ( )( )( ) ( )( ) ( )( )(801/226, -356/113, -801/226)-> B`= {( ), (37/9, 8, -29/9), (801/226, -356/113, -801/226)} BASE ORTOGONALa =( )‖( )‖( )b =( )‖( ) ‖( )c =( )‖( )‖( )-> B`` = {( ) , ( ) , ( ) } BASE ORTONORMAL