how to solve a system of equations?

I have this system: J(21x21) * X(21x1)=J(21X21) * B(21x1) - F(21X1).

I have to calculate the matrix X without using the 'inv' function X=inv(A) * J * B - A, X must have this dimension(21x1) .

The matrix J,B,F are calculated.

Answer 1

[Matt Fig]

% Choose some values:
J = rand(21);  
B = rand(21,1);  
F = rand(21,1);
% Calculate X based on J*X = J*B-F
X = J\(J*B-F)  % Here is what you want...
% Now check:
max(abs(J*X - (J*B-F)))  % This should be a small number.