ESCUELA DE INGENIERÍA DE PETROLEOS RUBEN DARIO ARISMENDI RUEDA
May 25, 2015
ESCUELA DE INGENIERÍA DE PETROLEOS
RUBEN DARIO ARISMENDI RUEDA
ESCUELA DE INGENIERÍA DE PETROLEOS
CHAPTER 4: ‘Direct Methods to solve lineal ecuation systems’
ESCUELA DE INGENIERÍA DE PETROLEOS
Types of Matrix.
1. RECTANGULAR:The Matrix that has different number of lines and columns mxn, Where ‘m’ is different of ‘n’.
2. Transpossition Matrix: Is the new matrix, that is obtain when the files and columns are changed.
ESCUELA DE INGENIERÍA DE PETROLEOS
3.Void Matrix. When all the elements of the Matrix are cero.
4.Simetric Matrix. Is square matrix equal to the trnsposition matrix.
5.Diagonal Matrix. Is a square matriz with all the elements cero except the element of the main diagonal.
ESCUELA DE INGENIERÍA DE PETROLEOS
6.Identical Matrix. Is a square Matrix that has all the elements cero except the element of the main diagonal that are 1.
7. Triangular. (Inferior or Superior)
ESCUELA DE INGENIERÍA DE PETROLEOS
8. Inverse Matrix. A matrix is inverse when:
ESCUELA DE INGENIERÍA DE PETROLEOS
METHODS.
SIMPLE GAUSS.
This method has two main steps.
a- Forward elimination: Consist in convert the Matrix into a Superior Triangular
b- Backward sustitution: With the Inferior Matrix the last unkown value is obtained and then we have to start making substitutions.
ESCUELA DE INGENIERÍA DE PETROLEOS
We can change the order of the lines to make it easier to solve
ESCUELA DE INGENIERÍA DE PETROLEOS
F2-3f1
f3-5f1
F3-2f2
ESCUELA DE INGENIERÍA DE PETROLEOS
NOW WE START TO MAKE THE SUSTITUTIONS.
ESCUELA DE INGENIERÍA DE PETROLEOS
GAUSS-JORDAN.
This method consist in treat the Matrix and convert it into a identical Matrix, and then is more easy to solve the system.
ESCUELA DE INGENIERÍA DE PETROLEOS
F1 *(1/2)
(F1*-3)+f2
(F1*-5)+f3
(F2*(-2/13))
(F3*-2)
ESCUELA DE INGENIERÍA DE PETROLEOS
(F2*17)+f3
(F3*13/96)
(F3*-1/2)+f1
(F3*-11/13)+f2
ESCUELA DE INGENIERÍA DE PETROLEOS
(F2*-3/2)+f1
x= 1y= -1z= 2
SOLUTION:
ESCUELA DE INGENIERÍA DE PETROLEOS
3. Inverse Matrix. The inverse matrix could be used to solve a system as well.
2x + 4y + 3z = 6 y – z = - 43x + 5y + 7z =3
THE SYSTEM COULD BE WRITTEN LIKE A *x=B
ESCUELA DE INGENIERÍA DE PETROLEOS
THE INVERSE
x= 25y= -8z= -4
THE SOLUTION IS