Page 260 - MATLAB an introduction with applications

Numerical Methods ——— 245

A = [6 3 6;2 3 3;1 2 2];
b = [30;17;11];
N = max(size(A))

% Perform Gaussian Elimination
for j = 2:N,
for i = j:N,
m = A(i, j–1)/A(j–1, j–1);
A(i,:) = A(i,:) – A(j–1,:) m;
*
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);
disp(‘matlab solution is’);
x = inv(A) b
*

OUTPUT is given below:
N =
3
Upper triangular form of given matrix is =
6.0000 3.0000 6.0000
0 2.0000 1.0000
0 0 0.2500
b =
30.0000
7.0000
0.7500