HP F2226A - 48GII Graphic Calculator User Manual page 356

The process of backward substitution in Gaussian elimination consists in
finding the values of the unknowns, starting from the last equation and
working upwards. Thus, we solve for Z first:
Next, we substitute Z=2 into equation 2 (E2), and solve E2 for Y:
Next, we substitute Z=2 and Y = 1 into E1, and solve E1 for X:
The solution is, therefore, X = -1, Y = 1, Z = 2.
Example of Gaussian elimination using matrices
The system of equations used in the example above can be written as a matrix
equation A⋅x = b, if we use:
2
A 3
4
To obtain a solution to the system matrix equation using Gaussian elimination,
we first create what is known as the augmented matrix corresponding to A,
i.e.,
Y+ Z = 3,
-7Z = -14.
4 6 X
2 1 , x Y ,
2 1 Z
14
b 3 .
4
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