Page 259 - MATLAB an introduction with applications

244 ——— MATLAB: An Introduction with Applications

b(i) = b(i) – m*b(j–1);
end
end
disp(‘Upper triangular form of given matrix is =’)
disp(A);
disp(‘b = ’);
disp(b);
% BACK-SUBSTITUTION
% Perform back substitution
x = zeros(N,1);
x(N) = b(N)/A(N,N);
for j = N–1:–1:1,
x(j) = (b(j)–A(j,j+1:N) x(j+1:N))/A(j,j);
*
end
disp(‘final solution is’);disp(x);
Output is as follows:
The final solution is
3
–1
–2
Check with MATLAB built-in function:
>> A = [2 1 –3;4 –2 3;–2 2 –1];
b = [11;8;–6];
>> x = A\b
x =
3
–1
–2
Example E4.21: Solve the system of linear equations by Gaussian elimination method:
6x + 3x + 6x = 30
3
2
1
2x + 3x + 3x = 17
1
2
3
x + 2x + 2x = 11
1
2
3
Solution:
Writing the equation in the form of [A]X =B and apply forward elimination and back-substitution
The complete MATLAB program and output are given below:
% A – matrix for the left hand side.
% b – vector for the right hand side.
% This performs Gaussian elminiation to find x.
% MATRIX DEFINITION