gaussian elimination solution method in matlab

To solve a system of linear equations using Gaussian elimination in MATLAB, you can use the rref function which performs row reduction to echelon form.

Here is an example code snippet that demonstrates how to use Gaussian elimination in MATLAB:

main.m
% Define the coefficient matrix (A) and the right-hand side vector (b)
A = [2 1 -3; 1 -1 2; 3 2 -4];
b = [8; -3; 6];

% Combine A and b into one augmented matrix 
augmentedMatrix = [A, b];

% Apply Gaussian elimination to reduce the augmented matrix to its row echelon form
reducedEchelonForm = rref(augmentedMatrix);

% Extract the solution from the reduced echelon form
solution = reducedEchelonForm(:, end);

% Display the solution
disp('Solution:');
disp(solution);
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In this example, we have a system of linear equations defined by the coefficient matrix A and the right-hand side vector b. We combine A and b into one augmented matrix and then apply Gaussian elimination using the rref function. Finally, we extract the solution from the reduced echelon form, which is the last column of the matrix.

Note that rref may return approximate rational numbers as solutions instead of exact fractions. If you need exact fractions, you can use the sym function to create symbolic variables and the solve function to obtain a symbolic solution.

I hope this helps! Let me know if you have any further questions.