Loading…

Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

Like this presentation? Why not share!

Dependencia lineal e independencia

on

  • 8,238 views

 

Statistics

Views

Total Views
8,238
Views on SlideShare
8,238
Embed Views
0

Actions

Likes
1
Downloads
44
Comments
0

0 Embeds 0

No embeds

Accessibility

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Dependencia lineal  e independencia Dependencia lineal e independencia Presentation Transcript

  •  
  • Definición 4.1
    • Un conjunto de funciones f1(x), f2(x),…fn(x) es linealmente dependiente en un intervalo si existen constantes c1, c2, … cn no todas cero, tales que
    • c1f1(x), c2f2(x),…cnfn(x) = 0
    • para toda x en el intervalo. Si el conjunto de funciones no es linealmente dependiente en el intervalo, se dice que es linealmente independiente .
  • Ejemplo 1 Dependencia
    • f1(x) = cos 2 x
    • f2(x) = sen 2 x
    • f3(x) = sec 2 x
    • f4(x) = tan 2 x
    • c1, c2, c4 = 1
    • c3 = -1
    • c1cos 2 x + c2 sen 2 x + c3 sec 2 x + c4 tan 2 x = 0
    • 1cos 2 x + 1 sen 2 x = 1
    • 1tan 2 x + 1 = sec 2 x
    • -1 sec 2 x + sec 2 x = 0  0 = 0
    • sec 2 x = tan 2 x + cos 2 x + sen 2 x
    Un conjunto de funciones f1(x), f2(x),…fn(x) es linealmente dependiente en un intervalo si por lo menos una función se puede expresar como una función lineal de las funciones restantes. View slide
  • Ejemplo 2 Dependencia
    • f1(x) = + 5
    • f2(x) = + 5x
    • f3(x) = x -1
    • f4(x) = x 2
    • c1 = 1
    • c2 = 1
    • c3 = 5
    • c4 = 0
    c2f2(x) = c1f1(x) + c3f3(x) + c4f4(x) 1( + 5x) = 1( + 5) + 5(x - 1) + 0( x 2 ) + 5x = + 5 + 5x – 5 + 5x = + 5x Es linealmente dependiente porque f2 puede escribirse como una combinación lineal de f1, f3, f4. View slide
  • Ejercicio 1 Dependencia
    • f1(x) = x
    • f2(x) = x 2
    • f3(x) = 4x - 3x 2
    1f3(x) = 4f1(x) - 3f2(x) 1( 4x - 3x 2 ) = 4(x) – 3( x 2 ) 4x - 3x 2 = 4x – 3 x 2 c1 = 4 c2 = 3 c3 = 1
  • Ejemplos Independencia
    • f1(x) = x
    • f2(x) = |x|
    • f1(x) = 1 + x
    • f2(x) = x
    • f3(x) = x 2
    • Gracias…