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amro Allhibi
amro Allhibi 2022-5-21
回答： Gangadhar Palla 2024-3-16
Problem 5.
Creating a function for GAUSS ELIMINATION METHOD. The Gauss elimination method is a procedure or numerical method for solving a system of linear equations.
a) Write a user-defined MATLAB function for solving a system of linear equations, [a][x] = [b], using the Gauss elimination method. For function name and arguments, use x = Gauss (a, b), where a is the matrix of coefficients,
b is the right-hand-side column vector of constants, and x is a column vector of the solution. b) Solve the following square system of four equations using the Gauss elimination method.
4x1 - 2x2 - 3x3 + 6x4 = 12
-6x1 + 7x2 + 6.5x3 - 6x4 = -6.5
x1 + 7.5x2 + 6.25x3 + 5.5x4 = 16
-12x1 + 2.2x2 + 15.5x3 - x4 = 17

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回答（2 个）

Image Analyst
Image Analyst 2022-5-21
Gangadhar Palla
Gangadhar Palla 2024-3-16
function x = Gauss(a, b)
% Check if the system is square
[m, n] = size(a);
if m ~= n
error('Matrix "a" must be square');
end
% Augmenting the matrix [a|b]
aug = [a, b];
% Forward elimination
for k = 1:n-1
for i = k+1:n
factor = aug(i,k)/aug(k,k);
aug(i,k:n+1) = aug(i,k:n+1) - factor * aug(k,k:n+1);
end
end
% Back substitution
x = zeros(n,1);
x(n) = aug(n,n+1)/aug(n,n);
for i = n-1:-1:1
x(i) = (aug(i,n+1) - aug(i,i+1:n)*x(i+1:n))/aug(i,i);
end
end

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