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Ejemplos
 

Ejemplos

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    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)