MATLAB: An example of using crammers rule or geuss elimination

#geuss #crammers

Just looking for a good example

Best Answer

Crammers
A = [ ...];
b = [...]';
[nr,nc] = size(A);
x = cram_rule(A,b);
fprintf('****************\n')
for i = 1:nr
    fprintf('  x(%d) = %5.3f \n',i,x(i))
end
fprintf('****************\n')
function x = cram_rule(A,b)
[nr,nc] = size(A);
DA = det(A);
for i = 1:nr
C = A;
C(:,i) = b;
x(i) = det(C)/DA;
end
Geuss
C = ...;
[nr nc] = size(C);
xn = [1:nr]';
[xn X] = gauss_elim(nr,nc,xn,C);
fprintf('****************\n')
for i = 1:nr
fprintf('  x(%d) = %5.3f\n',xn(i),X(i))
end
fprintf('****************\n')
function [xn X] = gauss_elim(nr,nc,xn,C)
% Forward Elimination
for j = 1:nr-1
for i = j+1:nr %row 1 pivot row
C(i,:) = C(i,:) - (C(i,j)/C(j,j))*C(j,:);
end
end
% Back Substitution
for i = nr:-1:1
sm = 0;
for j = nr:-1:i+1
sm = sm +X(j)*C(i,j);
end
X(i) = [C(i,nc) - sm]/C(i,i);
end
end
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