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HP 48gII User Manual

Page 356

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Page 11-30

Y+ Z = 3,

-7Z = -14.

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:

.

4

3

14

,

,

1

2

4

1

2

3

6

4

2

=

=

=

b

x

A

Z

Y

X

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.,

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