100408 13 Fase 2 Trabajo Colaborativo

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100408 13 Fase 2 Trabajo Colaborativo

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TRABAJO COLABORATIVO

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Fase 2 - Trabajo Colaborativo

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Aporte Trabajo Algebra Lineal

Ejercicios 5 y 6 Desarrollados

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TRABAJO COLABORATIVO FASE 2 - VECTORES, MATRICES Y DETERMINANTES

PRESENTADO POR DIANA RIOS YARURO CODIGO: 1.065.897.298 ANGELA MARCELA ARGOTE CODIGO: 1.065.830.763 WUINIS PAHOLA PARRA CODIGO: 1.065.658.321 YANETH REMOLINA CODIGO: 1.098.637.728

ENTREGADO A YURI VANESSA NIETO GRUPO: 100408_13 Sign up to vote on this title 

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INTRODUCCIÓN

Con el presente trabajo se pretende afianzar y reconocer alguno

aspectos que son fundamentales para abordar el estudio de algebr

lineal el cual se plantean los ejercicios prácticos para el afianzamient

de dichos conceptos planteados en el módulo de la unidad 1 d algebra lineal donde se abordan temas como vectores, matrices

determinantes donde se explica cada uno de los métodos de solució

para cada uno de estos sistemas planteados en cada ejercici

propuesto de tal manera que permite adquirir competencia

pertinentes para el estudio, análisis e interpretación de situaciones e el contexto de los diversos campos de formación disciplinar. Sign up to vote on this title

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Desarrollo de la Actividad

Ejercicios propuestos Fase 2 Vectores, matrices y determinan –

Desarrolle los ejercicios seleccionados y comparta la solución en el for de trabajo colaborativo.

1. Grafique en el Plano Cartesiano y luego encuentre la magnitud dirección de los siguientes vectores. a. El vector tiene un punto inicial y un punto fina

⃗      

b. El vector tiene un punto inicial

 

y un punto fina

Solución

a) (-3,2) (1,-4) -> (1,-4) (-3,2) (1-(-3), -4-2)You're Reading a Preview (4-6) Unlock full access with a free trial.

          √    *

Download With Free Trial

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b) (-2,-1) (5,2) -> (5,2)(-2,-1) (5-(-2),2-(-1)) (7,3)

          √    *

You're Reading a Preview Unlock full access with a free trial.

  

2. Dados los vectores:Download With yFree Trial a. U + V b. 3u + 2V Solución a)

⃗

, hallar:


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   

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3. Sean los vectores: Hallar: a. u*v b. ½ u * 4 w



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  ,

                    (  ) ( ) (     )              Solución

You're Reading a Preview

Unlock full access with a free trial.



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  (   )  *     *               4.

a. Hallar los valores de α que hacen que los vectores dados sean

ortogonales:

Y

b. Para el siguiente You're par deReading Vectores, determinar el valor de β qu a Preview hace que los vectores dados sean paralelos: Unlock full access with a free trial.

Solución a)




                 


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                      

5. a. Calcular b. Hallar

:



:

y



Solución


a. Calcular:

        


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   

6. a. Determinar una matriz de 3x4 que cumpla con la restricciones dadas.

    {    ,

b. Una pareja de conejos inicia su reproducción, donde ha nacimiento y mortandad, cumpliéndose la siguiente ley: Except en la posición a11, You're el número conejos que están en la granj Readingde a Preview es igual [4i*j – j] Unlock full access with a free trial.

c. Construya una matriz de tal manera que se den por lo meno 9 registros de datos del número Download With Freede Trialconejos y que cumpla l condición que j = i – 1 Solución Sign up to vote on this title



 Useful a. 3 x 4 = [aij ], aij = (i – 2j) si i no es igual a j,  y 1Notsiuseful i es igual a j

[a ]= 1

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Respuesta: [aij ]=

1 0 1

-3 1 -1

-5 -4 1

-7 -6 -5

b. Una pareja de conejos inicia su reproducción, donde ha nacimiento y mortandad, cumpliéndose la siguiente ley: except para [a11]= 2, el numero de conejos que están en la granja e igual a [4i*j - j], construya la matriz de tal manera que se de por lo menos 9 registros de datos del numero de conejos y qu cumpla la condición que j = i - 1. Para cumplir a condición de al menos 9 datos y j= i – 1, se construirá You're Reading a Preview una matriz de 4 filas y 3 columnas  3 = 4 - 1 Unlock full access with a free trial.

[a11]= 2 [a12]= (4((1)(2)) – 2) = 8 –Download 2 = 6 With Free Trial [a13]= (4((1)(3)) – 3) = 12 – 3 = 9 [a21]= (4((2)(1)) – 1) = 8 – 1 = 7 [a22]= (4((2)(2)) – 2) = 16 – 2 = 14 [a23]= (4((2)(3)) – 3) = 24 – 3 = 21 Sign up to vote on this title [a31]= (4((3)(1)) – 1) = 12 – 1 = 11  Useful  Not useful [a32]= (4((3)(2)) – 2) = 24 – 2 = 22 [a33]= (4((3)(3)) – 3) = 36 – 3 = 33 [a41]= (4((4)(1)) – 1) = 16 – 1 = 15

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7. a. Exprese la Matriz A como una matriz triangular superio haciendo uso únicamente de operaciones elementales:

             

b. Exprese la Matriz B como una matriz triangular inferio haciendo uso únicamente de operaciones elementales: You're Reading a Preview Unlock full access with a free trial.

Solución A=

2 1 5

1 3 -2

F3 = f 3 – 2f 2



-3

5

1

2


4 5 7

C1  C2

5

7–

2

-3 1 2

1 2 5

5 4 7

4

8=Useful 0  Not 1 useful-1

1

2


4

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24

b.Exprese la matriz B como una matriz triangular inferior uso únicamente de operaciones elementales. A=

2 3 5

F3 = f 3 – 4f 1 2 3 -3

-1 3 -4

8 0 7 5



-4

7 – 8 -4

32 = -3

0+

-3

0

-25

-1 8 3 0 0 -25

F2 = f 2 + 3f 1



2 9 -3

8 24 -25

-1 0 0

F2 = f 2 - 3f 3



2 0 -3

8 -51 -25

-1 0 0

-51 -8 -25

0 2 -3

0 -1 0

-3 3

9

6

24 = 9

0

24

-51

0

2 8 -1 c2 c3 9 24 0 -3 a Preview -25 0 You're Reading 24

0 Unlock + -9 0 trial. = 0 full access-75 with a free 8 Free Trial 2 Download With

-1 0 0

C2 C1

-51 -25

0 -3

f 1 f 2

f 3 f 2

-51 -25 -8

0 0 Sign up to -3 0 vote on this title  Useful -2 -1  Not useful

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          +      +                                  ↔

2

    +



                       



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                                

Respuesta

       +


b. De la siguiente matriz obtenga la forma escalonada reducida por Download With Free Trial reglones.

            ↔

  


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                                                                                



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                                                             



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        [ ]                                             





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                         Respuesta

9. Halle la matriz según el enunciado: a. Halle la matriz X resolviendo las operaciones de suma resta entre matrices} You're Reading a Preview

                           Unlock full access with a free trial.

b. Con la matrizDownload X del resultado halle la matriz Y With Free anterior Trial

 c. Con la matriz X y Y del resultado anterior halle la matriz Z Sign up to vote on this title

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                                                                                       



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=

b. Con la matriz X del resultado anterior halle la matriz Y. You're Reading a Preview



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c. Con la matriz X y Y del resultado anterior halle la matriz Z.

                                                (     ) (   )  (    )                           You're Reading a Preview




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10. Un cliente de un Supermercado ha pagado un total de $156 po 24 litros de avena, 6 kilogramos de pollo pernil y 12 litros de nécta de manzanas. Calcular por el método de Cramer el precio de cada artículo, sabiendo que 1 litro de néctar cuesta el triple de 1 litro d avena y que 1 kilogramo de pollo cuesta igual que 4litros de nécta más 4 litros de avena.

Solución

          +            || ||     | |         





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          ||||                 



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Solución del sistema de ecuaciones

Precio del Litro de Avena $ 1



Precio del pernil de Pollo $ 16 Download With Free Trial


Precio del Litro de Néctarde manzana $3 Useful  Not useful

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CONCLUSIONES

Con el desarrollo de este trabajo reconocimos y aplicamos lo

conceptos y ejercicios de la Unidad 1, cuyo contenido puntual es l

solución de matrices, vectores y determinantes el cual consta de una gra

importancia, ya que nos permitió resolver los diferentes ejercicio

planteados en dicha actividad mediante el cual se desarrollan la

capacidades analíticas y de pensamiento lógico basado en cada uno d los temas planteados en el módulo de algebra lineal. You're Reading a Preview Unlock full access with a free trial.



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REFERENCIAS BIBLIOGRAFICAS

Jeronimo, G., Sabia, J., Tesauri, S., (2008), Álgebra Lineal, Ciudad d

Buenos Aires, Argentina: Departamento de Matemática, Facultad d Ciencias Exactas y Naturales, Universidad de Buenos Aires.

Zúñiga, Camilo (2010). Módulo Algebra Lineal. Bogotá, UNAD Recuperado de: http://hdl.handle.net/10596/7193

Mesa, F., Alirio, E., & Fernández, S. O. (2012). Introducción al álgebr lineal. Bogotá, CO: Ecoe Ediciones. Páginas 5 a 18. Recuperado de: You're Reading a Preview

http://bibliotecavirtual.unad.edu.co:2077/lib/unadsp/detail.action?doc Unlock full access with a free trial.

D=10584265&p00=alg ebra+lineal


Tomado de: http://sauce.pntic.mec.es/~jpeo0002/Archivos/PDF/T06.pdf Sign up to vote on this title

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Hohenwarter, M. Hohenwarter, J. (2009). Documento de Ayuda d

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100408 13 Fase 2 Trabajo Colaborativo

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