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1
Class meeting #16
Monday, Oct. 18
th
GEEN 1300
Introduction to Engineering Computing
Excel & Visual Basic for Applications (VBA)
solving sets of linear algebraic equations
Gaussian elimination
1
Homework #7 due Wednesday
Classical Application of 2Dimensional Arrays
Solution of a Set of Linear Algebraic Equations
by the Method of Gaussian Elimination
First illustrate the method with a simple example
First, illustrate the method with a simple example:
123
x
2x
3x
0
4x
5x
6x
1
7x
8x
1
Shorthand notation: coefficients & constants only
2
0
456
1
788
1
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“Forward Pass” of the Method
1)
Normalize the “1,1 pivot” by dividing the
1
st
row by element 1,1
123
0
In this case, the first
456
1
788
1
row is already
normalized, but that
won’t usually be the
case.
3
2)
Reduce below the 1,1 pivot
0
1
Create zeros here
without changing
the fundamental
nature of the
1
equations.
2.1)
Multiply row 1 by 4 and subtract it away
from row 2, putting the result in row 2
4
45
6
1
481
2
0
036
1
()
3
2.2)
Multiply row 1 by 7 and subtract it away
from row 3, putting the result in row 3
2)
Reduce below the 1,1 pivot
Result
78
8
1
71
4
2
1
0
061
3
1
()
5
Result:
12
3
0
03
6
1
3
1
3)
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This note was uploaded on 11/07/2010 for the course CHEN 1300 at Colorado.
 '10
 CLOUGH

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