Page 216 - Excel for Scientists and Engineers: Numerical Methods
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CHAPTER 9 SYSTEMS OF SIMULTANEOUS EOUATIONS 193
If the pivot equation is normalized by dividing it by the coefficient of xJ, the
coefficient of x, is 1 and the calculations are simplified somewhat.
It will be instructive to show the progress of the calculations with a simple
example, such as the following:
The Gaussian elimination method operates on an n x n matrix of coefficients,
augmented by the vector of constants. In our example this matrix will be a 4 x 5
matrix, as shown:
: -1 1 165
First, row 1 is normalized: -
1 0.2 0.2 0.2 137
2 -1
3 -1
2 -2 256
5 -4
3 -2 361 -
The x1 terms are eliminated from column 1 of rows 2,3 and 4 by subtracting:
Row 2 is normalized:
The x2 terms are eliminated from column 2 of rows 3 and 4:
