How to Solve Linear and Matrix Equations in MATLAB?

Always use MATLAB's backslash operator \ (mldivide) instead of inv(A)*B. Backslash uses Gaussian elimination/LU decomposition, which is faster and numerically stable.

% Define system of equations: 3x + 2y - z = 1, 2x - 2y + 4z = -2, -x + 0.5y - z = 0
A = [3, 2, -1; 
     2, -2, 4; 
    -1, 0.5, -1];
B = [1; -2; 0];

% Solve AX = B using backslash operator
X = A \ B;

disp('Solution [x; y; z]:');
disp(X);