How should I use Cramer’s rule in Matlab?

Question

The relationship between the two matrices is shown is Ax=B.

How do I find x using Cramer’s rule?

A=[521 202 -176 612;-761 41 -655 712;314 102 -234 891;612 291 209 -318]

B=[718;408;215;356]

Solution

You can use Cramer's rule like this for your specific 4x4 case. The element at index i of the result x is given by the ratio of 2 determinants (See the wikipedia link for a full explanation) - you can create the result with the following loop

 x = ones(4,1);
 a_det = det(A);
 for i = 1:4
    C = A;
    C(:,i) = B;
    x(i,1) = det(C)/a_det;
 end

the column vector x should now be your result. There could be a faster way to do this but this should work. You can verify this by comparing the result with

x = A\B;