ME – 210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
Gauss(ian) Elimination
This is a
systematic
method in which (the coefficient of the) 1
st
variable is eliminated
(made equal to zero) from the (m–1) equations first, the 2
nd
variable is eliminated
from the last (m–2) equations then, and this process is continued until no more
variable and/or equation is left. Then, the solution is obtained in the reverse order
starting from the last one by a simple
back substitution
.
This is a powerful method which also yields all the information on the consistency of
equations as well as the uniqueness of the solution, if exists. The method has
several variants and some advanced versions. However, a very basic version of it
will be covered here.
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View Full DocumentME – 210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
The procedure is applied to the augmented matrix [A ¦ b] by performing a set of
basic (elementary)
row operations
, only such that the matrix [A ¦ b] will be
transformed into what is socalled as the
row echelon form
in which all elements
of [C] = [A ¦ b] below its elements c
ii
{i = 1, 2, …, min(m,n+1)} become zero.
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 Spring '09
 FarukARINÇ
 Gaussian Elimination, Row echelon form, Prof. Dr. Faruk, Prof. Dr. Faruk Arınç, Dr. Faruk Arınç

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