Applying Cramer's rule on an nxn matrix

I need to find the solution to a system Ax=b using Cramer's rule. It needs to be Cramer's rule. I have made the following code that works for a 3x3 matrix, but i want it to work for an nxn matrix using a for-loop.

I can't figure out how to write the loop.

Thank you very much in advance!

n=3; d=10;

A = floor(d*rand(n,n)); b = randi(d,n,1);

D_A = det(A);

A_1 = A;

A_1(1) = b(1);

A_1(2) = b(2);

A_1(3) = b(3);

D_A_1 = det(A_1);

x1 = D_A_1/D_A;

A_2 = A;

A_2(4) = b(1);

A_2(5) = b(2);

A_2(6) = b(3);

D_A_2 = det(A_2);

x2 = D_A_2/D_A;

A_3 = A;

A_3(7) = b(1);

A_3(8) = b(2);

A_3(9) = b(3);

D_A_3 = det(A_3);

x3 = D_A_3/D_A;

Answer 1

[Roger Stafford]

The two basic operations in applying Cramer's rule are: 1) replacing the k-th column of A by b and 2) obtaining the determinant of the various matrices which this produces, as well as the determinant of A. Hopefully you are allowed to use the matlab function 'det' for the latter purpose. The former one is accomplished in two steps by

 A_k = A;
 A_k(:,k) = b;

Of course you need to use a for-loop in order to do this for each k.

Answer 2

[Ali Jadoon]

Try this m file. It is general code for any size matrix to generate the output File ID: #45930