Page 138 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

v1=detd1/delta; % Compute the value of v
1
v2=detd2/delta; % Compute the value of v
2
v3=detd3/delta; % Compute the value of v
3
%
disp('v1=');disp(v1); % Display the value of v
1
disp('v2=');disp(v2); % Display the value of v
2
disp('v3=');disp(v3); % Display the value of v
3
v1=
17/7
v2=
-34/7
v3=
-11/7
These are the same values as in (4.34)

4.7 Gaussian Elimination Method

We can find the unknowns in a system of two or more equations also by the Gaussian elimination
method. With this method, the objective is to eliminate one unknown at a time. This can be done
by multiplying the terms of any of the equations of the system by a number such that we can add
(or subtract) this equation to another equation in the system so that one of the unknowns will be
eliminated. Then, by substitution to another equation with two unknowns, we can find the sec-
ond unknown. Subsequently, substitution of the two values found can be made into an equation
with three unknowns from which we can find the value of the third unknown. This procedure is
repeated until all unknowns are found. This method is best illustrated with the following example
which consists of the same equations as the previous example.

Example 4.11

Use the Gaussian elimination method to find v v and v, 1 2 , 3 of

2v – v + 3v = 5
3
2
1
– 4v – 3v – 2v = 8 (4.35)
3
1
2
3v + v – v = 4
3
2
1
Solution:
As a first step, we add the first equation of (4.35) with the third to eliminate the unknown v 2 and
we obtain the following equation.

4−20 Numerical Analysis Using MATLAB® and Excel®, Third Edition

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