Ejemplos
Upcoming SlideShare
Loading in...5
×
 

Ejemplos

on

  • 540 views

 

Statistics

Views

Total Views
540
Views on SlideShare
540
Embed Views
0

Actions

Likes
0
Downloads
0
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

Ejemplos Ejemplos Presentation Transcript

  • EJEMPLOS DE CÁLCULO DE MATRICES INVERSAS
  • Ejemplo 1: Calcular la matriz inversa de
    A=
    Ampliando la matriz a la forma:
    1 0 1
    0 -1 1
    -1 1 -1
    A I
    1 0 1
    0 -1 1
    -1 1 -1
    1 0 0
    0 1 0
    0 0 1
  • Realizando operaciones elementales de fila y de columna para obtener:
    ≈ ≈

    I A-1
    1 0 1
    0 -1 1
    -1 1 -1
    1 0 0
    0 1 0
    0 0 1
    1 0 1
    0 -1 1
    0 1 0
    1 0 0
    0 1 0
    1 0 1
    F3 = F3 + F1
    F2= F2- F3
    1 0 1
    1 1 1
    1 0 1
    1 0 0
    0 0 1
    0 1 0
    1 0 1
    0 0 1
    0 1 0
    0 -1 -1
    1 1 1
    1 0 1
    F1 = F1 - F2
    F2⇔ F3

  • ∴ A-1 =
    1 0 0
    0 1 0
    0 0 1
    1 -1 -1
    1 0 1
    1 1 1
    1 -1 -1
    1 0 1
    1 1 1
  • Ejemplo 2: Sea A= ,encuentre A-1
    Ampliando la matriz a la forma:
    a 1-a
    b 1-b
    A I
    a 1-a
    b 1-b
    1 0
    0 1
  • Realizando operaciones elementales de fila y de columna para obtener:

    ≈ ≈
    ≈ ∴ A-1=
    I A-1
    a 1-a
    b 1-b
    1 0
    0 1
    1 -1
    0 1
    a-b -(a-b)
    b 1-b
    F1 = F1 - F2
    F1 = F1 ⁄ (a-b)
    1⁄(a-b) -1⁄(a-b)
    0 1
    1 -1
    b 1-b
    1⁄(a-b) -1⁄(a-b)
    -b⁄(a-b)a⁄(a-b)
    1 -1
    0 1
    F2= F2-bF1
    F1 = F1+F2
    1-b⁄(a-b) a-1⁄(a-b)
    -b⁄(a-b)a⁄(a-b)
    1 0
    0 1
    1-b⁄(a-b) a-1⁄(a-b)
    -b⁄(a-b)a⁄(a-b)