Inverse matrix

In the development of systems of equations is an effective method using the inverse matrix so that the following is true.

[A][X] = [B]
[X] = [A]-1[B]
[A][A]-1= [I]

[A] -1 is the inverse of the matrix A and [I] is the identity matrix.
The basic calculation is to find the inverse matrix, but must have certain requirements for a matrix to have around:
• Must be a square matrix.
• The determinant must be nonzero.
There are several ways to calculate the inverse of a matrix, but in this case discuss three methods:

Direct method

From:Metodos numericos Grupo O1, Subgrupo 5, UIS

2. Method of gauss-jordan
This method extends the matrix with the identity matrix and gauss-jordan applied.
Example:

From:Metodos numericos Grupo O1, Subgrupo 5, UIS

From:Metodos numericos Grupo O1, Subgrupo 5, UIS

3. Matrix attached
In this process to find the inverse of a matrix using determinants and matrices transposed.
Example:

From:Metodos numericos Grupo O1, Subgrupo 5, UIS

Now you use [X] = [A]-1[B]

Example:

From:Metodos numericos Grupo O1, Subgrupo 5, UIS


Bibliografy:
• Steven Chapra, Métodos numéricos quinta edición.
• http://www.terra.es/personal2/jpb00000/tmatrizinversa.htm
• http://es.wikipedia.org/wiki/Matriz_invertible