How to Solve Linear and Matrix Equations in MATLAB?
What is the best way to solve matrix equation A X = B in MATLAB efficiently without taking explicit matrix inverse inv(A)?
John Michell answered .
2026-07-24
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);