gaussian elimination in matlab

To perform Gaussian elimination in MATLAB, you can use the built-in rref function, which stands for "row reduced echelon form".

Here's an example of how to use rref to solve a system of linear equations using Gaussian elimination:

main.m
% define the coefficient matrix and the constant vector
A = [1 2 3; 4 5 6; 7 8 9];
b = [10; 11; 12];

% combine A and b into an augmented matrix
Ab = [A, b];

% use rref to convert Ab to row reduced echelon form
rref_Ab = rref(Ab);

% the last column of rref_Ab contains the solution
x = rref_Ab(:, end)

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In this example, the A matrix represents the coefficients of a system of linear equations, and b represents the constant terms. To solve for the unknown variables (in this case, x, y, and z), we combine A and b into an augmented matrix Ab, then use rref to put it into row reduced echelon form. The resulting matrix rref_Ab contains the same system of equations as Ab, but in a simplified form with zeros above and below the pivot elements.

The last column of rref_Ab corresponds to the solution vector x, so we extract it using the (:, end) indexing syntax.

Note that rref returns a matrix, so the solution vector x is also a matrix. If you want to display the solution as a column vector instead of a row vector, you can use the transpose operator (') like this: x = rref_Ab(:, end)'.