Presentation of Gauss-Jordan Elimination Method I

University of Babylon

College of Engineering

Department of Environmental Engineering

Engineering Analysis I (ENAN 103)






Lecture Note

Solution of System of Linear Algebraic Equations

Undergraduate Level, 3th Stage



Mr. Waleed Ali Tameemi

College of Engineering/ Babylon University

M.Sc. Civil Engineering/ the University of Kansas/ USA



2016-2017



Gauss-Jordan Elimination Method

This method is used in solving systems of linear algebraic equations. It is similar to Gauss Elimination Method and as follows:

If the following equations are given and we asked to solve X,Y, and Z.
aX+bY+cZ=d (1)
eX+fY+gZ=h (2)
jX+kY+mZ=n (3)

Step 1: Transfer the linear equations to matrix form:
[?(a&b&c@e&f&g@j&k&m)]×[?(X@Y@Z)]=[?(d@h@n)]

Step 2: Rearrange the matrix rows and columns by multiplying any column or any row by a factor and add any row to any other row and any column to other column and/or replacing any row (column) by any other row (column) until making the value of the main diagonal equal to (1) and the values of all elements that located above and below the main diagonal equal to (0).
[?(1&0&0@0&1&0@0&0&1)]
Note that when you multiply a column and/or a row by a factor(s) and added to another row and/or column, the other side of the equation [?(d@h@n)]is also changed.
Result of step 2:
[?(1&0&0@0&1&0@0&0&1)]×[?(X@Y@Z)]=[?(r@t@s)]
Step 3: Solve the matrix equation and as follows:
X=r
Y=t
Z=s